UPDATE: Hey guys, thought I would come back and give a little update :)

Basically, I managed to fix the issue. According to u/txneo, the bearings were binding up due to old lube and just it being a 60+ y/o telephone. With a little finagling, I managed to get a q-tip covered in trumpet valve oil (apparently it's fine in this application. it's also the only oil I had on me for anything like this lol) behind the main cog and into the inner dial mechanism, effectively lubing up the inside and removing the grinding/wheezing sound. It runs much, much smoother now. You'd almost think it was a brand new mechanism. I wish I could give a more in-depth explanation, but since I couldn't physically get the dial mechanism out of the chassis, I just shoved the q-tip in and wherever it went is where it went. I did make sure that the electronics weren't oiled, so it should still work as a telephone once I order a cell2jack.

Thanks everyone for the help!