Superdestroyers:
Like most other warships, superdestroyers have a huge advantage against smaller ships. The thing is, in this case a ship of "equal power" is another supercapital. Since supercapitals are rarely deployed (the Shivans rarely deploy them too, even though they have like 40 of them) a supercapital on one side can allow them to instantly win a single battle, simply because the other side will probably be trying to fight it off with much weaker and smaller ships. That said, superdestroyers are extremely expensive. This makes it a bad idea for the GTVA to build one (that's what I said in the first place), but not for the same reasons you keep bringing up.
Solaris:
If the Hecate could be equipped with TerPulse, why couldn't the Solaris? The Solaris could probably carry more anyway, when you consider that it likely has a stronger power grid (being a much stronger warship). Retrofitting a Solaris with BGreens would be worth it becaue BGreens are still fairly powerful, if not as strong as the BBlue. It might also be possible to equip a Solaris with a LRBGreen, since that would apparently just require making a BGreen and then permanently increasing the amount of energy poured into it. That might not work though.
You would find space for beam weapons by removing some of its Apocalypses.
The Hecate's Terslash are innacurate, and they also have a poor field of fire (disregarding the forward one). The Solaris has an excellent field of fire, and if it can bring 4-5 of its Gattler Turrets (it can) to bear on a side attacker, it already has a heavier and more accurate broadside than the Hecate. This is ignoring the Solaris's Apocalypse, which give it far, far more firepower than the Hecate.
The Titan is superior in some ways, but it has a few noticable weaknesses: poor broadside, relatively weak armor (compared to the Solaris's), and weaker (and slower) torpedoes that can easily be shot down due to their small numbers. If you run a test in FRED, you'll see that the Solaris can easily beat the Titan if it flanks it and attacks it from the broadside. Attacking a Raynor in the same manner would deal serious damage to the Solaris, but the Raynor also has poor forward firepower. We also don't know how the Titan's hangar size compares to the Solaris's.
ECM:
I know from AoA that the Shivans haven't developed ECM abilities. Now, it's possible that they might have by the time they attack the GTVA again, but I doubt they will. It completely goes against their previous tactics, as the Shivans have always just tried to bury the GTVA under their superior firepower. On the off chance that they have, the GTVA's beams can also be jammed, and it would probably be no easier to jam the UEF's torpedoes.
Colossus:
It is true that, if the Colossus replaces all of its regular beam cannons with LRBGreens and flanks the Sathanas with its broadside, it will win the fight (though it will almost be destroyed itself). However, this requires overloading its beam cannons (which damages the beams), and even at that, the Colossus will take massive damage from the Sathanas. Considering that Colossus barely wins even with the huge advantage of flanking and even when it overloads all of its beams, it's really out of its league against the Sathanas.
Of course, the GTVA never expected to fight anything with anywhere near the Colossus's firepower or durability, so that probably explains the Colossus's general inferiority to the Sathanas. That kind of arrogance can be very dangerous on the battlefield.
I can guarantee you that the GTVA would not make that mistake again because they now have a much more realistic understanding of the Shivans' firepower and the Colossus's design flaws. Were they to build another one, they would make it better equipped to take on a Sathanas, because they now understand that the Shivans will likely always have something with equal or superior firepower.
Hypothetical destroyer-sized warship:
I'm not suggesting that the GTVA could match the Shivans' overwhelming firepower. That said, a warship like this would be useful because it would be a relatively cheap method of obtaining massive firepower, which is what the GTVA needs to deal with Sathanas juggernauts. They already have the ability to do so, but this would enhance that ability significantly, as this kind of warship would be cheap enough to mass-produce.
14th Battlegroup's fight with the Sathanas:
The Orestes might have been able to defeat the Sathanas on its own, but in the time that took the juggernaut could possibly have recharged its jump drives, turned around to attack the Orestes with its LRed, or called for reinforcements--the latter being most likely, and potentially a huge problem.
Ubuntu:
As for the Ubuntu philosophy being dangerous:
Remember that the Terran GTVA citizens are not happy. Ever since Capella was lost, they have been in a very bad economic situation, which probably means a lot of unemployment and very little beyond the bare necessities in live and all the while they see their Vasudan neighbors prosper. The only thing that kept the Terrans together and prevented mass riots all over the place was the goal of reuniting with Earth and that everything will be better once that happens.
Now enter the Ubuntu: The people affiliated with it (wether true believers or just allies like the Jovians) are very prosperous, healthy and well fed. Unemployment, if it exists at all, is very small. Their economy rivals the entire Terran part of the GTVA in a single system. For the downtrodden, poor fellows outside of Sol this must seem like paradise in comparison to their own place.
That is pretty much the picture of how it is, though with their information controll, the majority of GTVA citizens are propably unaware of it.
The average citizen will not think "Hey let's adopt the economical parts of Ubuntu and forget the rest", they will just think "Let's be part of it all the way". Now conside those not turned to the UEF. They will think that the 'new converts' are soft, short sighted idiots who traded their best chance for survival for a bit of luxury. In such a situation conflic is almost inevitable.
And with the Terran GTVAs economy already being on the brink of collapse, such internal conflict might very well be the final nail in the coffin sparking off widespread rioting and maybe even outright civil war.
Of course it's theoretically possible that this can be avoided, but the damage in case it does happen is just too catastrophic to wait and see, and thus the GTVA high command had to counteract the possibility somehow. They chose to counteract it by taking Ubuntu out of the picture and due to the unfortunate events at the end of AoA forced them into a prolonged war.
Remember that the GTVA didn't want that war. They wanted a quick and clean solution (well... clean from a strategic view... morally still ambiguous, but a lot less than the actual war), but between what happened to the 14th BG and it's vice admiral (Ad. Bei's 2nd in command... who's name I forgot) messing up, that was no longer an option.
The "average citizen" would not be fully or even mostly transformed by Ubuntu. This is because in order for a society to fully embrace Ubuntu, it would have to exist in a very special set of circumstances, and its citizens might even need to be conditioned from an early age to accept it (not sure about that part, though). In any case, the situation you described (some citizens adopting all aspects of Ubuntu and others getting really angry at them and possibly attacking them for that) would not happen, because even if lots of people tried to fully adopt Ubuntu, most of them would be unable to, as that would require a huge change in their personality. Look at real-life religions to see what I mean--many religious people follow their religion in name but not so much in practice (I'm not bashing religion, there are some that do.
). I know Ubuntu isn't a religion, but it requires a similarly huge change in personality to fully adopt it.
As for the UEF being under alien influence--that seems pretty likely, at least for the Elders. That may or may not justify the GTVA's invasion, however--If the Shivans are influencing them, they might well want the GTVA to destroy the UEF, partly because they hate Terrans in general, and partly because they would want the GTVA the waste their resources fighting the UEF and not have access to Sol's industries.
Damn, how did I get into seven arguments at once?