Problems involving Omega probably aren't useful examples for demonstrating your problem either way since Omega will accurately predict our actions either way and our identity angst is irrelevant.

I'd like to see an instantiation of the type of problem you mentioned above, involving the many explicitly dependant systems. Something involving a box to pick or a bet to take. Right now the requirements of the model are not defined much beyond 'apply standard decision theory with included mechanism for handling uncertainty at such time as the problem becomes available'.