Thanks for the continued advice. I might consider seeing a dermatologist at some point, more so to address other issues. In any case, I took a break from shaving yesterday and tried again today, and I have to say that I feel pretty great. I only got a tiny nick on my mustache that I didn't even feel, and I have absolutely zero pain right now. I did two passes WTG and I cleaned up the nasty patches XTG. I also used a disposable for some stray hairs at the very end.
I took a lot of extra time to ensure that I had a proper lather today and I think it helped. I applied zero pressure and I took my time. I got a surprisingly close shave for only going mostly WTG. I know that I'm supposed to stick to the same exact tools for at least a month, but I tried the aftershave splash just to see how bad the burn would be and it wasn't really bad at all.
I'm pretty happy right now and my technique is only going to get better. I'm glad that I joined this community because everyone gave some really solid advice and I'm well on my way to going from despising shaving to actually enjoying it.
Awesome progress! Know that you can do an aftershave splash and follow it with a balm once it dries. I'd still apply the balm every shave until you get it mastered. I still prefer balms and use them 95% of the time myself.