Yeah, I'm not really having any problems with the escalation, just with the avatar project constantly "HEY I'M TICKING UP YOU'RE GONNA LOSE SOON HEY HEY HEY HURRY UP" while I'm trying to get ready. I've got a lot of strong guys but they're wounded or occupied, I think I went into the black site too weak. The assassin's ignore overwatch ability really fucks me over, almost impossible to stop her from hitting a guy every round.
I got through the blacksite with no casualties and even took out the assassin, but then the last group of sectoids and the reinforcements just take my squad apart like we're not even in cover. This game is fucking exhausting.
If you're willing to start a new campaign there's an option to double the length of the avatar project timer, giving you more pips to work with before it's full. I don't think it ruins the game, but it does make it significantly easier because you have a lot of time to prepare before really going in. I agree the game can be exhausting, and if you ever feel like you're not having fun, it's often best to make little tweaks and find your favorite way to play.
The assassin is really troublesome at first, but isn't too hard to deal with once you know her shtick. You're going to take damage, so make sure you have a medic present and stocked; maybe even bring extra medkits on other soldiers. Keep your units separate, but not too far apart, to guarantee she doesn't do a crazy AOE ability to disable two or more of them at a time. Keep in mind you can reveal her while she's invisible if you flank her, so pay attention to where she runs off after attacking and flank whatever cover she's using. Then absolutely double down and do as much damage in a single turn as possible to absolutely delete her before she gets more annoying.
Also, battle scanners are your friend. They can reveal her location within an area if you chuck one.
Good luck, soldier.