Hi. I had a very similar problem. 1962 235. Ran great on the highway, could idle well for hours, sometimes would want to stall at a stop. Turned out that the throttle shaft was worn and the butterfly in the carb would close in a different place sometimes, and when it did, it wouldn't run right. On inspection, I could see the shaft was loose, and when I took the carb off, I could see the throttle plate closing in different places, sometimes covering the idle ports. I found a NOS carb on eBay and problem solved.

There is probably a way to drill out the throttle body and put new bushings in, or otherwise tighten up the fit. I oil mine periodically now to try to keep the wear down.

Hope this helps. Good luck.