Reloading tools are readily available for the 22 Jet. Brass is manufactured seasonally by Remington. Reed's sells a quality reload for the 22 Jet.
IF the 22 Jet cartridge doesn't really do anything for you, then an 8 3/8 model 17 would be just fine for your purpose.
To me wanting to shoot 22 LR out of a model 53 is a waste. I have many with the 22 LR cylinder and inserts, I will never use them. I have only fired the 22 Jet rounds out of any of my model 53s. The 22LR I save for my model 41s and 17s.