Firstly, the first two terraform improvements (I forget their names) only terraform the same exact tiles that the Ultra Terraformer will, but they are much cheaper.  You could just build those two until you get the Ultra.

OR ... more strategically ...

Since those two only terraform the exact same tiles as the UT, you can use them to gauge which tiles the UT can terraform versus not, and from that figure out non-UT-able tiles the other terraforming improvements can be applied to without wasting them on tiles the UT will eventually be able to terraform.

I've noticed that aside from biospheres which can terraform pretty much any tile, the UTs can only terraform the greatest number of tiles (as they are reusable).  HOWEVER, I have noticed that there are some tles the UTs _can't_ improve, but earlier terraformers can.  What I have started to do is wait until I've developed ALL of the terraforming techs.  Then I start with the UTs and place them everywhere they can be placed.  Then I check to see if tech #1 (Soil Enrichment?) can improve a tile that the UTs couldn't.  Seeing none, I check around likely tiles and replace the UT with tech #1.  Then repeat for tech #2, and so.  The last one I place is Biospheres because it is the only one that can improve a tile NONE of the other techs can improve.

On average, I maximize the number of improved tiles by 3 or 4 per planet this way, rather than placing the early techs first and doing the UTs last.  As long as it isn't an ice planet, water world, or lava field, that's a LOT of tile improvements per planet.

Which is a pain in the ass. The interface should make it easier to distinguish between the different qualities of tile, even if it's only "yellow means lesser terraforming devices can alter these tiles while red means only this level or better terraforming devices can alter these tiles," though better would be color-coding by terraforming level required.

It really doesn't help that the descriptions are very unhelpful.  Different techs will describe the 'quality' of tiles they can improve differently even when they are the exact same tiles.

"Planetary Soil Upgrade" and "Soil Engineering" are the two improvements that have identical tiles they can improve to the Ultra-Terraformer.  You can build one to free a tile, keep the other one around so you can compare subsequent terraforming improvements so you won't waste one that can improve un-UT-able tiles on a UT-able tile until you get the actual UT.

Once you get the UT, I suggest building PSU and SE first and the terraforming improvements that can work on non-UT-able squares, since they are much cheaper, strategically for maximum industrial output, build your starting factories and let them progress all the way to their maximum upgrade tech, and only after those factories have all upgraded do the UT since the UT is so expensive to build.  Trying to queue up the UT on a colony you just started will take several dozen turns per UT ... even if you put factories in the queue ahead of it, that'll only help a little -- remember the upgrade for those factories will get added to the end of the queue, so the factory upgrades won't build until after the UT if you stick UT improvements in your queue.  So even when I get the UT tech, I won't put it in the queue of new colonies until after I've built every factory I can and they've upgraded as much as they can.

I also intentionally stop adding any of the infinite projects (build research/wealth/influence/etc.) so that I'll get prompted of an empty planetary manufacturing queue when the factory upgrades are done.

Yes, exactly (on the second part).  But in the meantime, consider my earlier comment -- "Planetary Soil Upgrade" and "Soil Engineering" upgrade the exact same tiles as the UT.  They are the first terraform improvements you get ... so you can build one where its most strategically advantageous (to optimally improve adjacency, preferably for manufacturing) and leave the other as a guide for subsequent terraform improvement techs so you can see which can improve tiles the UT won't be able to (again since PSU and SE improve the exact same tiles as the UT, what they can improve, the UT can -- so if you alternate between selecting one of those and another terraform improvement, you can see which tiles the better terraform tech can improve that the UT won't).

Easiest change would be to color coded the terraforming hexes. Yellow = Tier 1, Blue = Tier 2, Red = Tier 3, something of that nature.