Everyone has mentioned Valkyria Chronicles, but you did not in your original post. Which means that you probably haven't played it, or you didn't like it (I find this to be highly unlikely).
Go play that. I find many elements of SRPGs to be unimmersive and that game singlehandedly shattered the wall between myself and not only SRPGs, but JRPGs in general. While I am still hesitant when it comes to turn-based or any form of non-real-time combat really, Valkyria Chronicles showed me what you can do when you blend fantastic, engaging and immersive ideas with a genre all about careful planning, positioning and command point-spending.
The third person movement is by far the best feature of the game and opens you up to real time death traps that you must avoid, and the aiming of your shots further adds to the feeling that the way you control your character actually matters (which is important to me, and this something that JRPGs/SRPGs tend to not have as a consequence at all). Having a slightly poorly aligned shot could cost you if your character's aim is not excellent and you shoot at the extremities of the aiming reticle.
It has perma-death, excellent classes and customizations, and just excellent gameplay altogether. It can also be punishingly difficult, I can't do many of the Extra Hard and Hard Skirmishes.
It also has gorgeous graphics, great characters, a good story and a brilliant soundtrack. It was and is my favourite PS3 game.
Anyway, the only other SRPG I'm tempted to try out is Fire Emblem: Awakening. It's far more traditional than VC, but I like the battle animation sequences and a game that is fairly simple to control is preferable for handhelds a lot of the time, I find. I've yet to try the demo, but I'll get my feet wet with the series then.
I really like the idea of strategy, I just feel sometimes it can be an altogether unimmersive or despondent experience. My example here is Disgaea. I could never play that.
<message edited by Satanas on Friday, December 13, 2013 3:29 PM>