From your original statements, it sounds like the JTV-59 is the one for you. You will feel right at home on that one.......though it is more of a "PRS" type feel on the right hand since there is not a separate bridge. I too own LP's, Strats, Teles, PRS, etc...... and using the JTV-59 is very natural. The neck feels very much like the neck on the Gibson Historic '60 Les Paul.....very much like that. Not slim and not chunky. Just right. And it is really nice to have that neck with the Tele and Strat models.
I know everyone has their own likes and dislikes, but I just can't get into the look of the other JTV guitars. I did own the 700 for a while, just did not like the neck on it.
I very rarely use a trem and the lack of it makes it much better for me. I would rather not have the trem than to have to tighten it down or block it. On a real Strat, I think the trem is an integral part of the sound, even if you don't use it. But, in this case, you plan to use a model, so the trem will add nothing to the sound if you won't be using it.
I may upgrade the tuners on my 59.....they are smooth but they don't seem to hold as well as some others I have. I bend the strings pretty hard. The nut could use just a little finesse right out of the box. But for a Korean guitar, it compares really well with the custom shop stuff that I have. That is a really strong statement!
And, then look at the pretty flamed top :D :D :D :D