I'd conclude from what you've described it's the starting circuit; it needs more fuel when cold but once warm the mixture is correct for the starting process. The best move would be to replace the cheapo PJ with a more sophisticated PWK, but that is only if you are going to keep it and don't mind spending $250 new or ~$100 used. I have the PWK on both of mine.
A new barrel is shy of 400 clams, a new pipe for your type of riding would run another 200. If you go that route then look me up and I'll cut that in a third. All I'd want in exchange is the $ and your exhaust. I ride in the SoCa desert so a big-hit delivery from the FMF is fine. millenniumdsj@hotmail.com
The barrel is coming off of my son's low-hour (original piston, in specs!) '90. It has a mellower hit than my '97; as a matter of fact it runs like an uncorked KDX or four stroke, having an even power delivery from the bottom to the top; mine has more snap and runs like a slightly underpowered, heavy flywheeled MXer. Being a young whippersnapper he wants my engine's characteristics so I'm putting on a newer barrel I ordered, and extra FMF pipe I have. I'd swap barrels with him but we don't do that much woods riding to justify tuning mine into soley a woods-oriented machine. And I'd hate to see his barrel go as I like riding his bike - the way it runs so cleanly in the woods, but then again we don't do that often enough to justify keeping it that way.
You may want to consider a Steahly fly wheel weight to smooth out the hit and minimize stalling, especailly when using the rear brake. I have one on each of ours since we do rock gardens in the desert and sometimes mountain single-track; makes it hook up better and tames down the delivery. You are welcome to try mine to see how you like it before spending the $.
There is nothing to be ashamed of in owning an RMX. It was the last asian 250 2-stroke enduro imported. Yes, they are not new tech and there are superior offerings from europe these days, but as a package and for a lot less $, relatively speaking, it delivers well-rounded, do-all off-road versatility.