Hey Heikki- Simplest would be to just use the '59 235 that you have found and stick with the stock transmission and rear-end if they work good for you. You may need a different flywheel to bolt to the 235, depending on which flywheel you have now. I can't remember, does your '37 still have the original '37 216? I think it did. If the '59 engine does not have the (2) studs hanging down on the front mount plate, they can be added or your 216 front plate can be used on the 235. On a '39-'40 truck you can move the radiator to the front side of the mount and use washers or spacers to shim the radiator ahead 1/2-3/4" to get some fan clearance. Maybe you could do something similar on your '37? As Jeff said, it does get very tight between the engine and radiator even with the short pump. An aluminum flex fan can help save space too.
If your wife doesn't like shifting the early 4-speed, you may want to try a '37-'39 pickup 3-speed. They shift easier. Or maybe adapt a '40-'46 3-speed in for the 2nd and 3rd gear synchros. Would take some u-joint and/or driveshaft work to get the later splines to match the '37 torque tube and rear, but I'll bet it could be done.