On a whim, I checked for a Ranco valve at my local NAPA store, and found there is a $10 rebuild seal kit for the H16 (and other) Ranco valves. I had a unit from an old car I parted years ago, with telltale signs of leakage into passenger compartment. I bought one of the kits and dug into the valve. You have to bend a total of 8 tabs to carefully take apart the valve and put it back together with the new seal in place, but it's not as hard as getting the old valve out of the car and putting the new one in.
You can ask your NAPA guy to look up a heater control valve for a 61 Chrysler and his screen will default to the kit. It's a NAPA Balkamp 6601000 Replacement Seal. I bought 2 of them at $10 each. After my initial repair of the old valve, I got up under the dash and got the original out, which looked much better than the old one I had just rebuilt, so I decided to rebuild the original and put it back in. Carl Bilter has a nice write up of his adventure getting the valve out of his 300J, but it's probably the same from about 59 to 64. One thing I would add to his write up is to take a string and tie it to the heat control end of the cable once you disconnect it from the push button control. That way, once you've pulled the valve down below the glove compartment and the other end of the cable has disappeared into the dashboard, you can pull it back out easily when you're doing the installation of the repaired valve. Took a test drive after putting things back and had one small leak at one of the hose clamps in the engine bay, but once I re-positioned the clamp and re-tightened it, all was well and no more drips into the interior. Hopefully it's good for another 58 years (and it won't be my problem then).
Hope this helps others who have had to just bypass their control for lack of a known fix.