On the 1DX, you can change to a different case by holding AF-ON or *, or both. I thought the same thing was possible with the 7D Mark II. As I don't have any, I just looked in the user's manual. If you do the same, and look at how to set up the AF-ON button, you'll see how to do that. It's on page 450 in the edition of the manual I have downloaded. You use the INFO button to access further details for AF settings.
This implies that you can have AF with one kind of characteristics with the trigger button, a second set of characteristics with the AF-ON button and a third setup with the * button. One of these could of course be "no AF at all", like on the trigger button, if you want back button AF only.
This makes it very easy to switch AF case on the fly, but also the AF point used, Servo/One Shot and the AF point selection mode (single point, zone etc.)
Yet another option you have is to allocate the Switch to registered AF function to a button. Unless you have a supertelephoto lens, the "cheapest" today being the EF 300 mm f/2.8L IS II USM, your only choice there is the depth of field preview button. This option implies that you can specify a set of AF setup details to be active as long as you keep this button pressed. Hence this can be combined with any of the trigger, AF-ON and * buttons used for focusing.
A third option is to apply the Register/recall shooting function setup to AF-ON and/or * buttons. You'll have to check in you camera which settings can be included there. I don't think they are listed in the manual, so I can't see what applies to the 7D Mark II.
OK, so My menu doesn't allow case selection, just the internal parameters. Well, if the change of case you want to do implies changing more than one of the inside parameters at the same time, then it's not convenient, of course. But perhaps some of the solutions provided in the paragraphs above will be sufficient?
It all implies learning a new method for working, but after a couple of thousands of practice shots with the 1DX, I think it was well worth rethinking a bit how I use my equipment. I spent a day at a racetrack a few days ago. Several hundred pictures, but in a way that was a waste, since only a single one was out of focus. That's not the kind of result I used to get a few years ago.