That's true, but as long as your own one is only queued somewhere you could destroy the foreign one, and it is refunded. Then you queue it also (and only) on that planet where your own is and then there are 2, and you can even finish them.
That way, eg. a SuperProduction world with multiple ManuCaps could be constructed, although you'd have to seriously delay the completion. In DA that was even possible with GA like eg the MCC^^^^
On the influence-stuff:
I've been rather unsuccessfull to find anything helpful on that matter. Initially I thought your observation about still-colonizable planets would do the trick, but then I wasn't able to reproduce it. I've gifted them a PQ1 at their homeworlds without result. All other planets will have very little effect as they would be fastly colonized...
I think the devs wanted AIP7 to be rather territorial, and probably thought that with their bad influence they would auto-loose distant worlds anyway, so why bother. The problem is that with TotA the occurence of habitable worlds got seriously reduced in comparison to a DA all-abundant map. And in smaller maps this zone is somewhat not distant enough.
Basically my main view is that the typical "bad-influence for badguys" thematic is ill-addressed, at least, from a balancing point of view. It hinders their colonization process, the Yors SA is disturbed two-fold: Not colonizing barren worlds, and having less zone of influence hinders the slowing-ships-trait. Korath spored worlds fall down permanently if other influences are present. Their Dark Influence is super strong if build on their core worlds, but doesn't really much if planets have 0.0n pop.
I was theorizing handing them an early + strong influence bonus which could aid them during the colonial rush - and afterwards taking that bonus away through a negative bonus that could be attribute on a basic tech, something they will always research (for example, Planetary Invasion). Choosing not to research this (and not being able to invade) is way more negative than an influence-loss. Although they shouldn't have the ability to circumvent that by techtrade etc, so probably one of their factory techs would be more suitable.
For Korath/(Drengin), an idea currently would be to transform their factory penalty from influence-->loyalty. Their worlds would fall equally but their zone of influence would be normalized.
But seeing your tests now with +200 prestige, well, why even bother....
Additional starbases will push influence. But the only thing that comes in mind is a reduced constructor-mod = more construcotrs = more bases. But that's Arcean style.
Or gift them more PQ so that at least they can make more out of their worlds, but then again that's Altarian/Arcean/Thalan etc thematic... Evil is more about destroying its worlds, as stupid as that may sound... (a concept that cannot work if the base game mechanics stay the same for everyone)