I’ve got a cox mix and match that’s been my favorite engine for many years. Recently I gave it new gaskets, new reed, new cylinder, piston, and glow head. I also put a bright yellow prop on it to go with the paint scheme on the model I intend to use it on.
I tried running it today and was frustrated at how problematic it was. I could feel it try to fire when I slowly turned the prop. It would fire and stop abruptly. When it did start it would only run 15 or 20 seconds and abruptly stop. It vibrated fiercely when it ran. Seemed like a hard backfire was stopping it. After several minutes of building frustration I stopped to think the situation through.
The engine had been a good runner for years. It dawned on me that the piston and cylinder was new and not broken in and should be treated that way.
I suspected the prop was bad out of balance so I changed it. I also changed the glow head. It started right up. I set it a little rich because of the new cylinder and piston. It ran rock solid and smooth till the tank was empty.
Basics - good prop, good head, good fuel  ...

Sounds like it was originally over-compressed.  Are the heads the same?  Depends on your nitro content, but it may have needed a couple more head gaskets.

  Well by my count you changed three things, maybe four? When making changes to diagnose a problem, change one thing at a time so you know what change affected the condition. it may also have been just something in the way you assembled it the first time. At the end of your post, you mentioned the basics, "good prop, good head, and good fuel."  Did you also change the fuel?
   Type at you later,
    Dan McEntee