The High Aldwin
FWIW, another issue with these types of systems is it makes AC 20 and 21 identical, because if you get a 20 on the first roll, you can't get less than a 1 on the second. If you want to say a 1 on the second is a miss, then AC 20 and 22 become identical since your minimum roll which would hit would be a 2...It's tangential, but when I think about it, I dislike that a 20 always hits and a 1 always misses. Is it silly to ponder something like, if you roll a 20 and it doesn't hit that you can roll another die and add it to your first roll to see if it was good enough. Similarly on a 1, roll another die and subtract it from your first roll.
To make it work, later rolls need to be 0-19 (or d20-1).
I think a nice way would also be to have the secondary post-20 roll be a proficiency die (+2 = d4, +3 = d6, etc.), because otherwise your chances of hitting higher ACs are almost guaranteed after the first 20. Which is probably why they don't do roll a second d20 and add to the first 20...