I had almost the exact same experience. The back and forth while spraying the gear mechanism with Liquid Wrench white lithium grease did the trick for me. I think I was able to pry open an edge of the gear box a little but maybe not. It's not been stuck since then and now every year I drop the spare and lube it some more.

I do not go off-road but the car is parked outside, no garage. I rarely drive it in the snow to avoid salt corrosion.

I agree that it looks like a real problem to replace. I found a YouTube video for a Land Cruiser and that cross member the gearbox is mounted on was bolted to the frame, not welded. A shame that Toyota chose to weld it on the T4Rs.

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