I forgot to post an update, but changing the transistor worked great. Speaker and headphone output work fine.
Some additional updates/information regarding my setup... I was using the SEX to power my desktop speakers, the Klipsch Promedia 2.1 system. I attached pictures below to show they're meant to be set up and how I wired them to make them work with a speaker amp.
When I hooked my Emotiva A-100 amp to the speakers, and they worked for a little while, but the fault eventually triggered. Eventually, the Emotiva amp would just go straight into fault mode after being turned on. I reached out to Emotiva, and they sent me a new amp and the SAME THING happened. The amp would work for a bit, then go into fault mode. Eventually, the amp would go straight to fault mode after being turned on.
I ended up buying a new pair of DIY speakers from parts express and have been using the SEX amp with it since and haven't had any issues. Was there something inherently wrong with the way I hooked up the speakers that could have broken 3 speaker amps? Or might there be something wrong with the speakers?