First caveat, I haven’t played a ton of this game, but I did (not to brag but I guess I’m doing it) get a 2-island victory on Normal on my first run; I’m only part way through my second run at the moment, with a different squad.
I think my style has been very similar to yours in a way—I prioritize the secondary objectives because that seems the best way to “get ahead” and actually power up for the end, but I’m also willing to sacrifice those objectives to avoid taking grid damage unless it’s relatively minor and I’m fairly confident I’m going to get it back shortly. So I focus on the secondary, but try to set up my plays to avoid grid damage, which means that I 100% let my mechs take hits unless they’ll die. Obviously, though, I don’t want to be standing around just soaking damage left and right just because, so that leads me to sort of prioritize mobility—whether that’s central positioning plus boosting movement capabilities; or taking abilities that make me more flexible in being able to strike anywhere on the map. Examples of the latter being the ability that lets you hit buildings with the artillery but not damage them, or the single-use bomb thing that can strike anywhere on the map. However, close on those types of upgrades’ heels is taking health upgrades so that I can soak more if needed.
Another major thing I focus on, which doesn’t seem to be the case with everyone based on streams I’ve watched, is knocking out those bastards who buff enemy health but don’t otherwise attack. In my mind, that’s a massive bonus for them that just compounds the more enemies you let hang around, so I’m totally willing to just manipulate the other enemies’ positions to delay damage in order to take those out first if I can.
Spawn prevention is a nice bonus if I can make it happen during my manipulation of enemies, as per above, but honestly I tend to do it more with my own mechs in line with the philosophy that I’m willing to soak hits.
I realize this is all a bit surface level given that I’m really speaking from a run and a half, but man do I love this game already and this is a cool topic to start—just wanted to throw in my two cents.
(It’s funny that you mention XCOM though, because I tend to play that game with way more of an eye toward just maxxing DPS and trying to clear enemies ASAP if I can; not what I’m necessarily doing here unless it’s a natural play)