It does sound like you may have cold control issues, but keep an eye on things before jumping to the same conclusion I did about my '57 GE Combination.
I don't think the defrost setting disables the compressor, but it should require the cabinet to warm up to the point where the ice will melt off of the evaporator before it kicks in again. I don't know anyone who has ever used the defrost setting. It's more a scenario of taking the bull by the horns and melting the ice through quicker means.
If cabinet temperature is holding at 37, that's good, but of course it shouldn't require constant running to do so. I think on any vintage refrigerator, a cabinet temperature of 37 should coincide with a cold control setting near the mid-range, or if anything, lower than mid-range. I'd be concerned if the fridge is running continuously to maintain 37 degrees, and isn't getting any colder than that.
There's no question that new gaskets will help, but I had a late 20's double-wide monitor top that lived in my parents garage for years and would fire it up when it was needed for overflow. The door gaskets were hard and brittle, even missing some small sections, yet that thing would keep things cold anyway, and didn't work hard at doing so.
I suggest setting the cold control in the middle and waiting at least a day for things to stabilize before checking temperature. Once you have established if the setting needs to be moved to colder or warmer, don't move it too far in either direction unless cabinet temp is way off from what it should be. If things are close to normal, I'd only move the control about half way to the next higher or lower mark on the dial, and wait another day to see what happens. It could take a week or more of playing with it. I'm entering week two of monitoring my Combination after removing and replacing the cold control I thought was faulty but turned out not to be.