My idea is to have the capital management be based on an orbital structure instead of a planet button.

Much of the game mechanics would be the same, with few differences.

I will call this structure the Orbital Capital (OC).

I think the Orbital Capital could have similar mechanics to a starbase. In other words, it would be a starbase with some notable differences. Suggested features:

• Every player starts with this already built on the home planet.
• Only 1 allowed per empire.
• Can be recreated if one is destroyed. 
• Built by the same ship which builds starbases.
• Can only be built on an owned gravwell.
• If another is built, the older is automatically scuttled.
• Center of the increased allegiance propagated from the capital. If this sructure is destroyed, empire-wide allegiance would slowly deteriorate until all planets reach the minimum allegiance levels. When a new one is built, allegiance slowly grows to the max levels
• Starts with much less hull/shields than a starbase. (like 1000)
• Starts with no weapons.
• Starts with the 'accessory government' bonus. This means that to take over the home planet, the orbital capital would also have to be destroyed. This reflects the importance of the capital / homeworld IMO.
• Race-specific bonuses would be the same of the starbase - remember, this structure would substitute and occupy the place ot the starbase on the home planet.
• Single military upgrade [ but with several levels ]: imperial bodyguard - to upgrade hull, shields, weapons and hangars. This leaves slots for other skills. Should be super-expensive to reflect that it improves all that stuff at once.
• Has the skill to build the Ambassador Ship, instead of the frigate factory. Makes sense to have an ambassador coming from the central government. 
• Also builds spy ships (see later).
• This is the target of the embassy skill. If the orbital government is destroyed, so are the embassies of foreign governments.

This could at the top level be as strong as a starbase, but I think it should be 20%-100% stronger, since it is the Capital, it should be the last stand of hope for an empire. 

The interesting stuff is:

A custom, 'makes-sense' place to build the Ambassador from.

A (hard to accomplish) way to try to cripple the enemy, since destroying it also damages max allegiance

The OC would have slots for Embassies around it. The Ambassador ship, to found an embassy, would target the OC and another satellite building would be created in one of those slots to represent the embassy. it would be colored with the embassy owner's color. The ambassador ship would be consumed, as the ambassador would settle in the foreign empire to conduct negotiations.

I am thinking on the idea that the embassy itself would have certain skills which can be triggered on the building when it is selected. 

This works both ways: The CO owner has the buttons which manage the OC upgrades in it, and when he clicks on the embassy, he sees actions that he can perform against the foreign player (embassy owner).

When clicking on the Embassy, the foreign player sees his own set of commands, which are not the same.

The actual commands would be dependent on what is actually available in diplomacy, and seems it is still maturing.

Command suggestions:

Steal ship plans. -  This would enable the player to copy the design of an enemy frigate or cruiser. The catch is that the player won't actually be able to use it in fight. It will just create a spy ship which will look like the enemy's, but without weapons. The enemy would see his own color on the spy ship, but the owner of the spy ship will see his own team color in it (and will be able to command it). Maybe a level 2 can give it weapons, but not the special skills, but it is not core to my suggestion. 

If the ship plan stealing stuff is too convoluted, the spy ship could simply have a cloak device which clones the visuals of a ship on the field.

Another skill could be detonating a spy ship to damage structures / ships. Terrorist stuff, you know.

Star bases, the OC and other spy ships should be able to identify a spy ship if it comes too close, but not necessaryly identifying the owner. Another (researcheable) level would enable to tell which empire was the actual owner of the spy ship by destroying it and examining the debris. Identifying the owner should increase a bad reputation 'spy' reaction modifier. 

Other (researcheable) skills which come to mind are:

• Bugging an enemy ship so that I can see the gravwell it is in. 
• The embassy is shut down when/if the players go to war, or many of the actions would be disabled.
• Spread propaganda to reduce culture growth/max allegiance.
• The OC owner should be able to disband/scuttle the Embassy if he never intends to engage in diplomacy with that empire again.
• The OC owner should be able to try to disseminate discord between two factions, if both have embassies in his OC. This would be disseminating propaganda so that both factions get negative modifiers against each other. 
• The OC should be able to cloud his capital gravwell, spreading disinformation so that the foreign players may see stuff which is not there, and not see stuff which is there.

Some treaties should only be possible when both empires have embassies on each other's OC, like military alliances (trade agreements?), while others can work with a single embassy.

I think there could be a synergic effect as well.

An embassy's effect would be smaller than those 10% points, but two-way. More embassies in contact with each other would gradually help improving relations. It could be a 4% increase for an embassy directly connected to a player, and 2% for an indirectly connected.

For example:

Let's have 6 players, A,B,C,D,E and F.

A has embassies on B, C and D.

B has embassies on A and C.

C has no embassies.

D has no embassies.

E has an embassy on D.

F has no embassies.

B and A have embassies on each other - direct links (4% + 4%); They also have embassies on C (2% indirect link). That accounts for 10% improved relations with each other.

C has no embassies, so A and B have 4% relation improvement with C.

A has a 4% improved relations with D. 

E has an embassy on C (4%), as a consequence A and B have a 2% improved relations with E - an indirect link.

F is alone at the corner, nobody loves him.

3 players allied would allow for a 12% bonus, and 4 players a 18% bonus. Beyond that is a very hard to accomplish scenario, but establishing peace with everyone and convincing them to make peace could be an interesting challenge. Maybe that could pave the way for a diplomatic victory?

There would be 2 ships then, the ambassador ship and the spy ship. In a nutshell:

Ambassador ship

• Establish embassy
• Spread propaganda
• Bug (targets ships or structures) - can see the gravwell target is in, for a set time.
• EMP (interrupts skills)

Spy ship

• Steal plans (chanelled, interruptible) steals ship layout; OR
• clone ship (cloaks the spy ship with the appearance and faction of another) 
• Sabotage (destroys ship)
• Bug (targets ships or structures)
• EMP (interrupts skills)