Well I went ahead and did it myself, and it turned out to be pretty easy.

I did in fact shut down the whole house before doing it, and I'm still alive to type this so all is well.

I replaced the AFCI breakers with a different brand than the one that was installed there. The one that was installed was Siemens, and the only other brand they had at the store was GE. So if you say GE tends to nuisance-trip as well, I could be in the same boat. I can mail-order some Square-D breakers if these keep tripping.

Note that there are no dimmers on these circuits, and the only thing that's ever turned on on those circuits when they trip are incandescent 60-watt light bulbs.