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Just thought I'd post an update on this:
I was able to remove the snap ring that holds the large ring gear to the OD mainshaft, then tap the ring gear back toward the main gear box enough to release the main shaft. After that, the ring gear slipped right off. I'm not yet sure what had everything so jammed up except maybe one small chip of metal in the ring gear.
Edit: It was indeed a small metal chip jamming up the ring gear.