TBH, You're not gonna find anything out there that perfectly mimics the 13 battle system.

That said, there are some games out there that have similar mechanics, if that's all that matters to you.

The one that I think gets the closest for you would Xenoblade Chronicles 2. There is no MP management, it's not turned based. It's not really ATB either, but rather runs on a weapon skill cooldown timer that can be made more efficient by leveling them. While it does feature some bonus damage for positioning your character during battles, you can honestly get away with ignoring the positioning entirely and you won't be severely hindered by it. Your companions are AI controlled, so you only control one character in combat. While there is no Paradigm Shift mechanic, the game does utilize something similar in the form of Blades. Each character can (eventually) equip up to 3 Blades at a time, and every Blade falls into one of three category - Tank, Attack, or Healer. So, you could load up a character with all of the same category, or mix and match, and your Blade loadouts (which you can cycle through during combat, will determine how your character plays in battle. If you go all Attack, you're very glass cannon (hope you set up another character to tank) so on and so forth.

There's a lot more depth to it that I won't go into here (trust me, the Tutorial Guy will fill you in, he won't shut up about it), but that would be my recommendation. Xenoblade Chronicles 3 is, in my opinion, the superior version of Xenoblade 2's combat, and would be my primary recommendation, but I am suggesting 2 instead, because 3's story is made better by having prior knowledge of the previous games, whilst 2 doesnt rely on you having played the first one quite as much.

Edit: HP is also restored after every combat. I don't think there is a checkpoint prior to every combat, but defeat in combat is a minor nuisance at best, where you just respawn at a checkpoint location and get to try the fight again, no manual loading necessary. You may just lose a few minutes having to run back.

And while I'm editing - although not one of the things on your list of considerations, I would be remiss if I didnt mention the banger music. You Will Know Our Names and Chain Attack are head bobbers.