M7 chances? non-IB/PE profile

What do you want out of an MBA?

Since you don't have prior PE (or even IB) experience and just no name consulting/corp strategy, buyside is going to be a very, very low chance from MBA... even if you land HSW which I think is pretty unlikely. PE/GE are not likely paths, anyone coming in post-MBA is expected to have a few years already on the buyside and significant deal experience, know the process well from start to finish and be able to quarterback a deal - not just writing memos and doing some diligence. VC maybe depending on your network, but unless you land Stanford I'd argue you're better off trying to do that move from your current seat if your firm does a lot of venture work in the space you want to be in.

Between that and your kind of unclear goals - mentioning dual degrees that don't open any incremental doors and only make sense in very unique situations, wanting to use this to get to politics - your story doesn't make a ton of sense right now and I don't think it is going to resonate with adcoms. 

With your current story I'd say very little chance at HSW, some chance but not sure thing at the lower M7 and may want to look into top 15 if you really want to go to MBA soon.