02 Chev Silverado 2500HD - transmission replacement

ORIGINAL ISSUE:

My truck is binding/shuddering in reverse only. I replaced the entire rear differential, carrier, ring/pinion, etc and still have the same problem. The transfer case has fluid. Put it in 4-low and couldn't put it back in 2-high. Had to put the transmission in reverse to put it back in 2-high. ...

UPDATE:

I can shift it in and out of 4H and 2H just fine. I cannot, however, get it to go into N or 4L. I kinda forced it into N, then it wouldn't go back to 2H until I put the transmission in reverse like I did before. I "shifted" it in and out of all the gears while the new transfer case was still on my porch to make sure it was good. The transmission was in neutral and stopped while I was attempting to go to N and 4L on the transfer case. It's the floor/mechanical shift for 4WD, not the electronic version.

And....it's still shuddering/binding up in reverse. I don't know what to do now and I'm kinda running out of money at this point. Considering taking it to a Chevrolet dealership for diagnostics. Or, would replacing the transmission fix the issue?