What do you mean plays weird??? That doesn't tell us sh!t!
As in flatter radius of the neck? Or flat "note" or pitch-wise? Either way.... now I'm surely confused. You say it plays weird, then "it's not that terrible either"! Your sounding more like a girl trying to decide whether to wear the red ribbons or pink ribbons in her hair! You know..... "eeww... which ones? Such a dilemma! What do you think?"
I guess you realized your 350 and the JEM had different pickups. If so, did you really think they would sound the same? Look, it's not uncommon for a player to buy an insturment and change pups to alter the tonal characteristics of it. Some will prefer a slightly weaker pickup too. Or with a different frequency curve based on it's windings and type and placement of the magnets.
Evo's can be "harsh" to some players not used to a hot pickup. Some change them out for the EVO II or Breeds. It's all personal preference. Trial and error. Go to the DiMarzio site and read up..... You'll be surprised what you'll learn.
Changing the string gauge is going to make some difference in how the guitar feels (ie. stiffer to play as in doing bends will require a little more hand strength, better "tone" as in the string will be slightly "boomy-ier" and will have a degree of better sustain characteristics) But you're right, it's not going to be the "fix all" you seem to be fixating on!
And if it "plays worse" well..... you're just screwed!
Sell the JEM cheap and write it off as buying something with no real direction in mind.
But that's hard to understand since you say you played "nearly every Ibanez in the store". I'll bet some mighty fine instruments passed through those hands and because you really didn't know what you were looking for, you threw money away! But that will make you a music stores favorite kind of customer! So there is a "positive" for someone!
Look, trading for the PGM probably isn't going to make much difference here since it seems you don't have any real understanding of what your looking for or why you need another guitar! Odds are you'll end up in the same boat but with a different set of complaints.
As far as a trem.... I believe your RG350 has one, Yes? What's the problem with that guitar? You seem to like it?
So here's the real "skinny" on your question..... it's probably not going to "rectify" your problems. It may actually intensify your problems. The guy setting up the guitar may set it up to his preferences which may or may not be to your liking. You may have tuning issues you haven't experienced before. The pups won't magically change to your liking. The neck "flatness" isn't going to suddenly develop more of a radius..... the list goes on!
Bottom line would be to learn more about the guitar you already feel comfortable on (your RG350DX) figure out what the neck spec's are (look on-line at the Ibanez web site) and look for something comparable. I'll bet there is something in the Prestige line that will suite you fine. Guys buy new guitar for many many reasons..... Musicians buy new guitars for only a few select targeted reasons. They need a different tone completely! (wood species, type of guitar solid body compared to semi hollow body etc.) They want a change in neck feel. (from a Les Paul, to Strat, to Ibanez) They have plain wore there current one out! (only to buy the same model) And lastly..... "it looked cool" and they knew they could adapt to it!
Of course your other option is to start modifying your RG350 with some new pups, work in the trem and make sure it's operating to max efficiency. Buy a Blank pickguard and set it up so the controls are exactly where you like them.... all things you could have done with the cash you dropped on the new JEM. Besides.... you'd have had some extra left over for a new set of .10's! Just a thought!