Appreciate the insight so far everyone! I don't have a clamp meter.. I've been meaning to buy one for general around the house shenanigans, so I ordered one today (Paid $4 overnight shipping, thanks Amazon!) so I'll be getting it tomorrow! I'll test the current as it's leading up to popping it's thermal fuse, and see if that provides anymore details.
@Tautech
The motor doesn't seem to feel too warm to the touch, or smell burned... but to be fair, who knows what the last owner did or did not do! One thing I've read with these compressors, is people bypassing the thermal overload switch all together and just running it, I was tempted to do this to see if it pops my circuit breaker too. But alas, I wasn't thrilled with venturing into the unknown without asking a more knowledgeable bunch.

@alsetalokin4017
That was my initial hunch, that they would be very close due to the tolerances, I just wasn't sure how far the tolerance should really be off with motors. You know how it is when you're looking for information and not very knowledgeable on the subject, it's easy to get sucked into misinformation/over complicating stuff when you're reading! I'll be yanking the capacitor tonight and testing the capacitance, I only have a low-end ExTech 430 but should be sufficient. (of course, after discharging said capacitor

)
@kleblanc
The only reason I didn't really think it was the start capacitor, the motor seems to start with no issues (no sputtering/bogging down, etc) and run for up to 5 minutes. I can constantly reset the thermal fuse to keep it running. I was under the (limited) impression that the start capacitor leaves the circuit when the motor begins to turn. (Potentially the centrifugal switch on the motor that Kevman mentioned, more below)
@Kevman
No comment, good ol Harbor Freight for you! In regards to the centrifugal switch, I did read that as potentially being the issue as well. My thought on that though... if the start capacitor was stuck in the circuit, it would have (visibly?) blown long ago, correct? After reading/watching videos about these capacitors, start capacitors generally have a very low duty cycle and will blow if in circuit for more than a few seconds. (I assumed this after watching this TEMCo video
)
Thanks again guys, I'll be checking the capacitor tonight and report back, then tomorrow I'll be testing the current!