And to give an answer in a slightly different direction:
One style of using quickcheck is to compare the actual system to a simplified model. I think that kind of approach would probably solve the issues you’re describing.
It sounds like you’ve been trying to write properties saying that “for any random input, ensure that all adjacent pairs of buttons differ by exactly 1”. As you’ve noted, current limitations of elm-html-test prevent you from inspecting the HTML in a way that allows you to do that.
To use an approach of comparing to a simplified model, you could instead write a function that takes the random input and produces the expected list of buttons. That function is your simplified model, and your real view function is the real system. Your fuzz test would then take a random input, use the simplified model to get the list of expected buttons, and then assert that all the expected buttons are present in the Html produced by the real view.