Precision Transmissions has by far some of the best videos out there.
I was wrong on one of the specs. Originally I was going say 425 was the rating, now I'm looking at 410 being the factory rating, but I said 350 pound feet, conservatively not to lead anyone astray. Basically the TH350 can handle 300 to 425 or a little more pound feet of torque rated engine with little or no problem.
On the output bushing... Those were changed so would be ok. The slip yoke actually rides on the bushing and as long as that is all tight as far as spec, you shouldn't have much "wobble".
The following is a guess, but pic attached is the rear planet and these do fail and can cause the problem you have. Not a guarantee, just a possibility.
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The pic below is the high performance unit that has the five pinion setup, plus a lower gear. This unit can handle more power and changes 2.52 first gear to a lower 2.75 first gear. The 1.52 second gear ratio will stay the same. Third gear is still one to one.
View attachment 222447