Your best bet is a Mustang-11 front kit. Any of the street rod guys should have a universal kit. Keep the stock frame, it will save a ton of work. You can also keep the stock front end, but add disk brakes and a mono-leaf spring. Add a open drive line and late model rear axle with mono-leaf spring and you know have a lowered, smooth riding, modern front independent front end, with power disk/drum brakes, what more do you want?

The S-10 frame is a close match, but will require some adapting. The problem you are going to find is the cab and nose of the '37 is very narrow, and not many truck frames will fit. Joe