Thanks for everyone for the advice! It's now just barely playable!
I would do more searching around too. I got some ini advice (somewhere...) that fixed some stuttering I was having really well.
So I had a UFO defense. I was actually caught off-guard, because after evading it the first time around I figured it wouldn't come back. Well it came back for more, and in South Africa X-COM made what might be its last stand in Operation "Winter Giant". Our AO was a forest near some overgrown buildings (and a cemetery, love that). The Spike o'doom was behind a large building, so that complicated our efforts to make this easy. Having been caught off guard, our turrets didn't have an engineer in them, but nonetheless we had four of them and they performed admirably all things considered (barring one; I momentarily had options to move my turret, and after trying that it wouldn't work anymore). My original plan was to send in my Grenadier with some minor support backing him upwhile the rest of the team supported from behind: the plan was to blow up the building and allow the snipers to take out the spike. It didn't work. My forward elements got pinned down quickly, and within a couple of turns almost me entire team was pressing forward to help him (barring my sniper, who managed some sweet shit with serial and killzone). Unfortunately, the weren't fast enough, and my beloved grenadier got taken down before the rest of the team could support him (more on that poor son-of-a-bastard later). New Plan time: my rangers and WAR-suit Gunslinger went forward to attack the spike from around the buildings, while the rookies (and one barely-trained Psionics trooper) Bradford was sending me led by my surviving Colonel Grenadier (who was a heavy gunner) and my Specialist Medic held the middle area and pinned down reinforcements.
The Spike wasn't very concerning, but the troops holding the area proved to be more resilient then I expected, and we took relatively severe injuries. After taking down the spike, my forward elements retreated while my middle troops continued to rain hell on the reinforcements. Unfortunately we were just beginning to get over-run, so I ordered a general retreat of everyone but the few who couldn't make it to the hanger in time. A mis-click cost me a rookie at around this point. This is also the point where the turrets started paying for themselves, as they both hit the MECS hard and took the occasional shot for the team. My WAR armor gunslinger took the last of the hard hits (I finally have a chance to use the Shield-Wall ability), while someone retrieved my bleeding specialist from the Elite Lancers (I've had exactly two bleed outs this entire game, and it was the same guy both times; dude doesn't want to die). By the end multiple people were in serious shit: one of my rangers had exactly 1 hitpoint left, others were burning to death, and the only person who didn't take damage was my sniper (and maybe like one or two people here and there).
RIP Denis "Junkyard" Pavlov, my Hard-Luck, balding, former EXALT Grenadier. An inglorious end for someone who an old cynic. Final mission statistics tell me we took down 43 out of 46 of the bastards, in exchange for 6 wounded and two dead. Statically a good match, but still painful. Fun though, very exciting and tense.
Anyway, with that the resistance now wants to attack the Hunter UFO that they brought down. Ordinarily I would do something else, but I could use some revenge. After that I might try and contact the remaining regions before going for broke. I have more then enough breathing room on the AVATAR project currently, so I don't need to rush.