Unless the planet in question is an asteroid, there is always a region where your ships can exit phase space and be outside of the SB's range. For instance, if the SB is on one side of the phase lane, order your ships to execute their phase jump on the other side of the lane. You can also order your ships outside of the gravity well so they exit phase space outside of the other gravity well.

Right now, I can tell you that you're too heavy on capital ships - you can get away with this against the AI though. Credit for credit, frigates have better damage output than capital ships, especially long range frigates - the reason one fields any caps is to make use of their abilities.

An alternative to Ogrovs are Bomber strike craft. The AI is generally unable to deal with large numbers of Bombers and given that the AI's Fighters are suppressed/not too numerous, they can chew up the SB equally well.

If you want to make sure your ships run over as few mines as possible, set their engagement ranges to "Hold Position". This way, they will only engage targets that either enter their weapon range, or ones you ordered them to attack.

Those 35 Kodiak Heavy Cruisers will rip apart most frigates, but if the AI is fielding enough bombers of its own/you are not fielding many fighters/flak, they'll burn pretty quick.

Generally, the AI's capitals will target enemy capitals first, so if you have a large number of long range frigates, simply order them to all focus their fire on one cap at a time while the capitals duke it out. IIRC, the damage modifier for the LRF damage type against the capital armor type is 75%, which is actually one of the higher modifiers (most other ships do 25% or 50% damage to capitals, Bombers to 75% as well, only other capitals do 100% against capitals).

There is a complete table of damage modifiers in the Strategy section, which basically will show you what counters what.

Edit: the thread containing that table is Combat Mechanics, one of the stickied threads.

I plan on making more Hoshikos. They really helped me last time, when my Akkan, Kol, and eight Kodiaks and twelve Cobalts beat two Radiances, a Revelation, and five Destra Crusaders. But not without losing all my Cobalts, half of my Kodiaks, and almost lost my Kol.

I also plan on making at least 15 more Kodaiks.

Really? I didnt know that they didnt hit so hard.

Anyways, I want many CS there because they can take a lot of damage. My Idea is to use them to divert attention away from the Ogrovs as the Ogrovs pound the SB into oblivion. Even if I lose a few CS, I will still have defeated the SB, which will make my job a lot easier. If im lucky, then i can defeat the enemy fleet and the SB with my current force.

Just pick one side or the other, jump in and fly out of the starbases range.  Use your fleet to guard your Ogrovs, and then blow up the starbase from long range.  You might lose a few little ships, but that is why they invented post mortem military commendations and promotions.

If you move to the edge as far as you can go on your gravity well and on either edge and then jump in you should be out of SB range. Other thing is that if sb doesn't have spin and meteor upgrades you should be able to bypass sb without being wounded to heavily....... you could also build your own sb in their grav well and then build docking booms to replenish your hoshikas with antimatter. Ai is stupid and will attack first ship that jumps into grav well. 

If you have lvl 6 akan with armstice jump in engage ability bypass sb with your fleet and build your own sb. SB should be half build before armstice runs out...... 

Hell you could move directly to the sun and build sb there. Once one is operational if you build another 3 in cluster with previous one and arm them with docking booms they are impenetrable deffence for ai.... Just leave akkan in to extend their range and to try to kill your akkan ....

Heres the latest intel on enemy strength and my fleet strength:

Do you think this is enough?

You:

500 command - capital ships
500 command - heavy cruisers
60 command - support cruisers
140 command - long range frigates
168 command - carrier cruisers
80 command - flak frigates

Total: ~1450

Opponent:

600 command - capital ships
340 command - heavy cruisers
148 command - support cruisers
84 command - long range frigates
380 command - carriers
20 command - flak
44 command - light frigates

Total: ~1600

We can ignore the Ogrovs and Adjudicators.  Keep your Ogrovs out of the fight and jump in to clean up the starbase once you have things under control.  You have two big threats here.  The first is his carrier force, and the second is his Progenitor/Iconus combo.  This is far more dangerous than the Radiance and Revelation you were talking about earlier. 

Because he vastly outnumbers you in strike craft, make sure you dock your bombers.  Use a staggered flak burst (manually time it) with your three Kols to thin out his numbers before launching your bombers.  As rowanlad suggests, more strike craft would be very useful.  Meanwhile, focus your combat units on knocking out his iconus guardians.  The AI probably won't use repulsion (and if it does, it won't use it very well) so this should be feasible.  Make sure you focus fire on specific targets; those five Progenitor Motherships will give his fleet massive shield regeneration so if your damage is spread out you won't even scratch his units.

The levels of the capital ships are always the wild cards, but if these were human-controlled fleets, I'd be betting money on the Advent player at this stage of the game.  He has to screw up for you to win.  Fortunately, the AI is absolutely terrible in combat, so you should still be able to squeek this off.

So how many more light carriers are we talking about? Ever carrier holds two suadrons, so Im guessing another ten is enough? And more fighters or more bombers?

Anything else I need?

As with anything, there's a tradeoff.  More fighters will help you clear out the enemy bombers more easily.  More bombers will help you clear out their heavy cruisers more easily.  Personally, I'd go for a 25/75 fighter/bomber split, keeping my bombers docked in the early stage of the battle until my Kols get to work and clear the enemy strike craft, then launch my bombers afterwards.  With three Kols, you can afford to go light on fighters.

If you are using a mod, you need to say so, because that does change matters.  IIRC, DS capital ships are considerably more powerful than in the regular game, if not downright overpowered.

Not sure how they trade of against bomber but if you don't mind to reload last save you can always try and see how they fare.

And Darvin is right. DS caps are much more powerful and it boils down to how mush upgrades did you manage to research compared to enemy (hull, shield, weapons, AM regen) since every tier has at least 4 research upgrades..... Is in DS as well or not???, but do you have option for weapon shied negation research, If so that will benefit u a loty against those progens. 

But i still think your best option 4 sure victory is to jump in with sb constructor as well build sb and fight untill his fleet is killed near your sb. Just get rid of those starfish first.

Didn't play DS for a long time but again if I'm not mixing with some other mod there are fighters that disable abilities on enemy ships. Not sure if it is TEC or Vasari though.....

Given a target the AI determines it can destroy easily, it will eventually send a fleet over that it thinks is sufficient to overcome the planetary defenses. What you can do is pull your fleet out one phase jump away to another one of your planets, but have them ready to jump back. Given time, the AI will send a scout in, see the fleet defending the planet is gone, and will try to take the planet by sending its fleet in. At that point, you can jump your own fleet back in to take on the AI fleet with home field advantage.

With that said, put up Phase Jump Inhibitors so as to deny the AI fleet a quick retreat should they decide they can't take on the combined firepower of the planet's defenses and your fleet. Once you reduce the AI fleet to floating wreckage, the AI has fewer ships available to cause you grief when you launch your own attack.

This game roughly boils down to he who has the me SC wins. Sad statment but sadly true.

the fact that you are playing the distant stars mod is incredibly important...

The way you would apporch the situation is so incredibly different than in regular sins that... almost impossible to compare.

If i were you, i would take the easy way out, buy myself 2 more marzas, (up them to lv 6), 2 more donovs (also up them to lv 6)... go in as far away from the sb as possible, popping off armistice if nessasary if thier starbase has those evil advent specials, go camp out on the side of the gravity well, the enemy fleet will react, pop off a flux field, as thier strike craft get into range, pop off your kol's lv3 flack bursts, (you DID get flack burst right??), wait for thier massive fleet to show up, have the kodiaks/bombers focus on the cap ships, use your donov's emp to drain their shields and antimatter to almost nothing, and fire off your 3 marza Missle barrages.  Dead enemy fleet. finish off the caps.  send the bombers after the starbase while your caps bomb the planet.

watch the preety nukes.