Thanks everyone for your help and input. Wanted to update you all with my solution and leave it here for future owners who encounter the issue.
I tried to drill it out with a
Grabit bit. I wasn't having success, probably just my technique. I was using a drill and the bit just kept removing material from the stripped screw/bolt without actually biting in and moving the bolt at all.
I went to the dealer and talked to the service head about my issue. He said when they do front axle changes on these machines (2013 1025r), they don't bother with the vent plugs because they frequently strip and cause the time-consuming problem I'm experiencing. He said just remove all drain plugs, the fill port, and let it sit for 2 hours. It all comes out eventually.
Removing this bolt seemed unnecessary to complete the fluid swap and had high potential to cost lots of time, tractor downtime, and potentially money. I made the decision to do as the dealer does and leave the plugs in, especially because this fluid swap is only performed every 600 hours. With the plugs left in, the fluid drains and fills more slowly, but the job can still be done. It's only in the last quart or so of filling that you start to have overflow issues related to lack of venting. Perhaps you could insert a flexible hose, small diameter, into the fill port as a vent, and fill faster. I used a kitchen fluid measurement cup, 16 oz, to pour extremely slowly compared to using the 1 gal jug the fluid comes in.
My tractor will just live out its days with a vent plug that looks like this on one side, and I'm okay with that: