I've been using the same setup as the author for about a year, I can help some.

1. I don't know, never tried this. I do know iCloud backups still work, because I've used them after wiping my phone. But I think you must plug the new phone into your computer and set it up as a managed device before you load the backup, or else parts of the profile might not take.

2. No, it's not. I traded in my old macbook pro for a mac mini back in May. I was able to use Apple Configurator on the new mac mini to change the profile on my phone. There is one caveat though -- the phone is still technically supervised by the old mac, so you have to confirm the profile by going into the phone's settings. Using the original, you just have to plug the phone in and unlock it.

Thanks for the reply, appreciate it.

Both of your answers sound workable for me!

Even if I couldn't restore the whole profile from backup while traveling (which seems natural), at least it's still possible to restore some data. Which should be enough in the short term.

And that's perfect that I could manage it from a different Mac. That totally works for me. I worried there would be something which prevented that. I'm imagining a parent using this for parental controls, but then the kid disabling it at a friend's house who has a Mac. Works better for my scenario though!