There's a video on YouTube https://www.youtube.com/watch?v=pDsTcrRVNc0
about a looping layer models, after watching that I poured some thoughts off the top of my head into a comment which, of course, promptly sunk without a trace. I'll repost the gist of them here.
If you gain benefit from looping layers, at some level every layer of parameters is in front of and behind every other, the conclusion must be that the order of the layers does not need to be fixed at all.
If you cycle through the layers multiple times, are you doing so for the benefit of a particular layer on a particular problem. If so, can you skip the other layers that don't add on repetition. If you can skip (and you can know when to skip), and you can repeat (and know when to repeat)
What you would need is a mechanism which can decide which layer is needed next. Is that then not a looping single layer MOE model? Storing the layers as a wide set of selectable options rather than a deep set of unconditional layers. You would be picking what the next layer should be (or exit the loop) the threshold for exit drops each iteration so it always eventually exits. With a tunable 'how hard to think' knob to adjust the threshold.