On my first set of attempts, I too got into that endless boot process. For me it was because the system was so messed up that it would not see the Wireless Keyboard CMD+R keys before the Apple Logo popped up and installer restarted.
My solution was to get out my old USB keyboard from an ancient iMac and use it for the restart with CMD+R. It did not miss holding down the keys on the USB keyboard and went right into the recovery screen. It was a relief but not really a surprise. I thought about using a USB mouse too but all you really need is a good read of the CMD+R keys before the Apple logo pops up and then it's off to Recovery. There it actually reads the wireless mouse and keyboard just fine.
Regarding Apple Support:
One thing that seems to help with Apple Support is that I always seem to have one or more gadgets on an Apple Support contract ... and because I'm on the Automatic upgrade program, Apple Support is always current for my iPhone. I think showing up as an Apple support customer when you call, might help with priority, even if that particular product is not under contract.
Having said all of that, a 'Saturday' appointment makes it sound like they're swamped by installation problems, so I'm not sure even an Apple Support customer will get instant service.
But give the USB keyboard a try ... any USB keyboard will do, so just borrow one from a PC if needed. On a PC keyboard, I think the Windows Key = Command but I don't have one to try.
The good news is the systems isn't really bricked. The BIOS is working so the problem is that it's redirecting to the installation loop because there's no external command to stop it. If it were bricked, the screen would be Black, white or just a mess of garbage.