Here is some closure for our organization's issue:
After working through this with ESRI (who was very responsive, BTW), I also learned that Field Maps (and I think Collector) do not support maps with repeated layers in them. They will work with layers/view layers, just not the original hosted layer added twice. So, after editing our maps to remove the duplicate layers, we are able to open them in Collector and Field Maps, but not Collector Classic (which as Glen stated, is not unexpected). As an organization, we are transitioning to Field Maps.
I still find it odd that the maps with duplicate layers worked fine in Android and older iOS versions, but I guess this is just the impetus we needed to switch to Field Maps. 🙂
-Mike