Sounds like an MBE4000 for sure. I worked for the dealer for those during their heyday with detroit. In my professional opinion, they suck. For more reasons than just the turbo.
Eaton autoshift or Allison automatic. Tranny is one of those two no doubt as mentioned. Either will do the job just fine if they're in good shape.
I think its an Allison though. It would be a 3000 series in that size and year of truck. Lock up clutch in the converter doesn't waste any more fuel or power than would be expected. Truely and strongly recommend useing genuine Allison Transynd oil in it. Yes it is more expensive than regular ATF. but YES it is that much better for the longevity of those transmissions. Plus transynd allows extended drain intervals too.