Pretty much any trans can be used behind a 4bt, using various adapters. My 4bt came with a Chevy adapter, so most GM transmissions would bolt up. It had a TH475 (commercial version of the 400) behind it. There are also Ford adapters. The Dodge flywheel housing bolts right up- the 4bt and 5.9 are essentially the same motor except for length. You can also find SAE adapters to use commercial transmissions, such as Roadrangers and the Deuce's Spicer.
The Dodge 5-speed (NV4500) isn't a large transmission compared to many of the other alternatives. I don't have experience with the M37, but I think the NV4500 would most likely fit in quite well. If you use a 2wd NV4500 with a divorced transfer case, the trans is actually pretty short. I have one on hand and could post pics and dimensions if you want. I was given (no kidding) a good one out of an early 90's GM truck. Its a 2wd with the rare granny 1st gear. I don't know what its going in, but I'll find something!
For NV4500 selection, there are a few options. If you want highest strength, use the Dodge Cummins version. It has larger input and output shafts. This one is found in the diesel and V-10 trucks. There is the Dodge V-8 version which has smaller input and output shafts. Then there is the GM version , which has different shafts than the Dodge version but is similar in strength to the Dodge V-8 version. My Durango uses a custom setup which is a V-8 Dodge tranny with a diesel input shaft so I could use a Dodge Cummins flywheel & clutch. The gas version has a 27 spline output shaft which let me use the stock Durango transfer case. This has held up fine.
Ask any questions you want. I don't get on here a lot, but I'll try to check back.
Jim