Fender Richie Sambora Strat
The trem - making it a full floating trem might affect the tuning if anything as you trem will now not rest against the body as I'm assuming it does now... but it will have to support itself with the string tension. *I don't know who makes the FR on that guitar, but chances are it's not the best one. *You may want to look into getting a nicer one. *That's the only possible problem I see.
The neck - Warmoth necks are built to fit ONLY (ONLY!!!) Fender bodies or Warmoth bodies. *They have how to measure the neck pocket to be sure on their site... check it out. *It should fit your guitar fine.
As for tuners... just get some used fender ones probably. *If that guitar has a locking nut as I'm sure it does, the tuners aren't gonna be HORRIBLY important.
Warmoth also has good descriptions of neck radiuses if I remember correctly. *If you want an Ibanez feel, go for one fo the flatter ones.
However (you probably saw this coming)... by the time you're done with this... couldn't you have sold the guitar that isn't what you want, taken the extra money, and just buy one that is what you want? *It's gotta be close.