Huge success
Pulled the passenger axle and slid the intact axle from that side, loads of nasty came out with it... Thankfully the axle doesn't look bad on that side and the initial shake on the hub was nice and tight. I'll still open it up and inspect the bearings/brakes/seals on that side as well to see whether I think it looks rough or what. Axle tube drooled a little oil when the flange came off, but less than I'd have expected.
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Crawled under the rear end and evaluated the removal options. Turns out the spiders gears are WAAAAY less effort.. 1 little friendly bolt vs 4 big ugly bolts and really important things to not drop or get upside-down/backwards, etc. It wasn't a hard decision.
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Once that was done, it was just a matter of choosing the appropriate drift to push the broken section through the carrier and out the passenger side. I went for the blue one with a broom on the end since 1) I hate that broom, and 2) it was the only thing with the right combination of length and diameter on hand.
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A bunch more nasty came out with the broken axle, though none in the differential so it appears to be coming out from the passenger side tube, awesome. I'll force a couple shop rags down there to try and get that crud out before I put new juice in the axle.
I didn't take any pictures of the removed shaft because it is just a rod covered in grime, not that exciting to see. Plus, I promptly wrapped it in garbage bags and stuffed it in my hatchback to take to the parts place tomorrow at lunch after I got it out.
I'm headed to get the replacement axle tomorrow and likely a bunch of bearings/seals and play the reassembly game. Guess I should read up on the pack/don't-pack wheel-bearing camps.