Double-posting for an update.
Swapped out the rear oxygen sensor with a new one. I suspect the heating circuit in my original sensor was malfunctioning, and this seems to have solved the initial bad readings at startup. Problem being it didn't solve the issue completely.
Fuel pump, ignition coils, spark plug, rear oxygen sensor have been swapped. Any other ideas? Might swap the front oxygen sensor. Last error I saw was p0597 (which doesn't make a huge amount of sense to me). No p0137 error anymore, so at least there's that. Might also clean out the throttle body again, though I doubt it'll help.
EDIT: Update: The only code being thrown is the p0597, so I've ordered a replacement engine coolant thermostat. The bucking has been gone for a few days (still throwing the p0597 code once in a while though), I suspect either the current thermostat has completely gone, or it/whatever the problem really is is just giving my some time off. Part will show up in a week or so, hopefully I'll swap it out the weekend after this coming weekend and all will be well. If I replace it and don't see the problem again I think I'll be home free, else I'll swap the front O2 sensor, though I doubt it is a problem..
FINAL EDIT: Everything's fixed. I'm not sure if the thermostat was influencing the bucking, judging by how nothing seemed to change when I swapped it out (aside from getting rid of the error code it was throwing). The car started throwing the error code for the front O2 sensor after replacing the thermostat, so I swapped out the front O2 sensor as well, and now all is well. It's been 1.5-2.5 months since I swapped the front O2 sensor, and no issues whatsoever. All is well.