Gas oven thermostat

I'm not really sure this is thermostat problem. This range is O'Keefe and Merritt and is probably from the 50's. I've recalibrated the oven thermostat many times, probably every 2 years or so since I started using it almost 25 years ago. You pull off the oven knob and there's a screwdriver adjustment for the calibration. A few little twists and some patience and I've always managed to get it working right again.
It used to take around 10 minutes for the oven to go from room temperature to around 350 F. Now, for some reason it's just not the oven it was. It takes about 15 minutes or more to reach 350.
After calibrating it very patiently, the best performance I'm getting is this:
I set it at 350 and after 10-12 minutes the gas turns off, obviously due to the thermostat action. But it's not even 300 then. However, not touching the knob, some 10-15 minutes later the oven is 350 - 375. I'm pretty sure if I leave it on longer, it will get up to 400.
Years ago, a few times I had problems because the gas jet (where the gas meets the air and the flame comes off) was evidently clogged and the oven would stall before reaching the set temperature because the flame hadn't reached all the way around the oval gas jet. I resolved that by running a brush over the gas jet (when cold). However, I checked recently and the gas is all the way around, so I don't know why it's taking so long to reach the set temperature.
Is there anything I can do for this? Is this a thermostat problem? Do I want to look for a replacement thermostat? There's a used appliance store nearby and I could probably get something from them, but wonder if it would be the right part. I suppose I could bring mine to the place for comparison. Maybe I can get a part number off mine. Or can I order one? Thanks for any information or suggestions.
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