This recurring random difficulty argument is getting stale already... Sure Psi can mess you up and it happens "randomly", but the AI moving to the right place to kill you is also random, the AI spawning at the right place to mess you up when you disembark is random.
You can take measures to lessen the likelihood of the AI walking to the right place to kill you, and you can take steps to reduce the likelihood of psi messing you up, like arming recurring targets more lightly, or isolating them.
Much like you can favor a certain playstyle to reduce the chances of getting "random" owned by shooting (play in smoke, always move in a certain way to maximize mutual surprise, camp&snipe), you can also adapt your playstyle to minimize the odds of psi randomly messing you up. Being more aggressive, adapting the spread of your gals and your weapons to the situation all helps with psi.
The easiest way to make sure you won't kill yourself when MC'd or panicked is to use poison gas ammo and armors immune to smoke damage. Then with stun gas to take captives and poison gas to kill the troopers very efficiently, you're only left with the few enemies that are immune to smoke (probably only the provost? Espers aren't immune. Cyberdiscs are probably immune, but flamethrowers make cyberdiscs a joke, while they aren't great against gals, especially indoors since it has no range). Then the only chance of losing a soldier is if it is MC'd and the AI walks it past the frontline to a place where you can't save it, which is more due to bad planning on your part than anything.
Can you loose soldiers occasionally to Psi? Yeah, sure, but it's far from common. I lose much fewer gals to Psi than to shooting, or a failed melee rush. If you're complaining about Psi and haven't met star gods yet, good luck. And good luck to your computer, you'll probably smash it in frustration.
Vanilla Psi is terrible, but Piratez has gone very far and made it much more manageable. Hopefully this topic won't come up all the time..
As for the original ideas: More variations, especially in late game, would be nice.
I consider an invisible chryssalid to be much more "obnoxious difficulty" than Psi. It will randomly mess me up here or there depending on where it spawned, or will turn the game in a "scan every other step just in case" game, which is not something I consider enjoyable. Star Gods/Cat girls and their funky invisibility already kind of push it, but they're not fully invisible and are either the end game enemy, or very soft.
The academy mecha sounds cool.
The guild superheavy tank sounds bad, just cranking up armor and damage doesn't make a unit very interesting to me. High armor means you need your weapons to roll higher to do damage and I despise having to spam units with the best guns I have and just getting zeros, then the next time killing another in 3 shots that happened to roll high. Medium armors, good resists and lots of HPs is the way to go as far as I am concerned. You get durability without the randomness of outcomes when tackling one.