Ken, I have a 1937 1/2 ton pickup and based on my experience, here's what I think you have.
I'm assuming this is a stock truck with the original transmission.
Your transmission synchronizers are worn out. You can find out for sure by draining the transmission oil. Most likely you will see small particles of brass in the oil, especially at the bottom of the transmission. The reason the transmission oil is low is because it has drained back down the torque tube to the rear axle; caused by a worn out seal (called an "Okie Bushing" by some) at the top of the torque tube, behind the transmission, which is designed to stop the oil from draining down the torque tube to the rear axle housing.
If you pull the filler plug on the rear axle, my guess is that the oil will come gushing out. If all of this is true, your transmission does need to be rebuilt.
By the way, it ran nice and shifted good until the transmission oil got hot and thinned out. Up to that point, the synchronizers were being slowed down enough by the thicker, colder oil in the transmission case and thus acted like they were functioning as designed. When the oil got hot and thinned out the synchonizers no longer functioned correctly thus showing their wear.
Some people add "oil thickner" such as STP, or a like product, in hopes the thicker "blend" will slow the synchronizers down and cause the transmission to shift normally. I tried that and it didn't help me, so I would not do that if someone suggests it to you.
The transmission needs to be rebuilt and if you plan on keeping the truck and the stock transmission, I would rebuild it with the newest gears available. By this, I mean use cross cut gears instead of the strainght cut gears the transmission most likely has in it now if it is stock and has never been rebuilt. I would look for a good set, or put together a good set, of 1954 gears, which will be much better than the 1937 gears. The only difference is that you will have to use the 1937 transmission output shaft because the universal has a 10 spline on a 1937 truck and the output (and universal) on a 1954 transmission has a 17 spline shaft. This is not a problem, just be sure you do it or you will not be able to complete the installation of your rebuilt transmission. It will shift easier with the cross cut gears and the overall satisfaction/enjoyment rating of the transmission will be higher and, thus, better for you.
If your neighbor says he can rebuild it, suggest my ideas to him and see what he thinks. That might help you decide if he is a good canidate as a rebuilder.
Whatever you decide to do, you'll have to do something, because it isn't going to get any better.
I hope I have helped you! Good luck!
Joe
