Dave, sweet truck, i have a thing for the 37 gmc as I have a T16 that i bought when i was 14. If i recall i saw this truck for sale on the Hamb for a good price, glad you got it and have plans to keep it decent vs a rat rod. anyway, i digress.
as far as shortening the wheel base, i was able to do it to mine way back when, the gmc has an open driveshaft and i removed the solid non slip section of driveshaft and used a cold chisel and 4lb sledge and took the heads of the rivets holding the spring hangers on the frame off. I then slid the springs and axle up that amount. I drilled and bolted with grade 8 bolts and it gave me a 115" WB if i recall.
I am also wondering what model yours is for sure, mine is a T16 and it has the vertical louvers on the hood sides and a different emblem and 3 horizontal trim pcs that are over the louvers. Yours has the later general motors truck emblem like on the 39-40 and no louvers. I bet you have a bit heavier gvw, or maybe a canadian truck?
As for an engine - easiest to fit would be an I6, although i shoe horned a 396 BBC in mine useing the factory steering box and a set of headers.
I see that your grille is banged up, i made new vertical bars out of solid aluminum. I am possibly going to make some of the curved horizontal ones too. if you want, PM me and we can discuss making some for your truck
good luck
jason