Thank you all for the help. After replacing the starter relay and driving around for a day and a half it looks like the problem has been solved

When I removed the relay the plastic cap was loose and the circuit board slightly exposed. Maybe moisture was getting in and messing with the contacts or something. I'm not out of the woods yet but I don't remember going a whole day without the issue happening at least once.
Learned a few new tips for changing the ignition switch too. Going through the A/C vent is way, waaaay easier than from under the dash.
Sometimes I wonder why I do the things I do

Someone told me that the relay was integrated in the starter, so I went with that and replaced the starter first (it was dying anyway) then the clutch and ignition switches. A simple Google search or forum question would've told me in two minutes that the relay was separate and to start there...
But hey, at least I also fixed that broken A/C vent too