if they are going through wood framing that is required to be fire or
draft stopped with insulation or foam, derating factors apply if there
are more than 2 cables (NEC 3334.80).

Speaking of insulation, the wall that will get all these outlets does
have insulation (fiberglass) between each of the studs (its backside
is into an attic space). From what I can tell, the original wiring
was wired over the top of the insulation (its very thin, so fits
between the wallboard and the middle of the stud where the hole and
cable is). Since then a previous homeowner laid thicker pink
fiberglass insulation against the wall between the studs. Is there
any issue with these wires being that close to insulation? I would
intend to run the new wires like the old ones (between the two layers
of insulation).