There isn't really another option than the one proposed to you unfortunately.

Might get some marriage proposals on the internet with that resume :) I don’t want to bring the bad news but you won’t get 5% down unless you are going to live in it as a primary residence. 

Clearly understood by ALL partiesFor your situation I would propose this to your aunt:-50/50 profit split.  

Now we're facing a variance if we rebuild in the existing footprint of the house and a likelihood they won't approve our proposal.

I have not seen the proposals yet.

Sounds like you need the advice from a local professional real estate agent who can provide you accurate values for the proposed bedroom increase.

A local attorney may be able to take a proposed Order to the judge's clerk and get it signed ex parte while the judge eats lunch. 

The note assumption (a very attractive proposal) is simply a transfer of debt that would not affect the 1031.Your client will need to purchase $550K ish in new real estate using $160K ish of cash.  

You should definitely look more into seller financing that way you can propose options to them, maybe that way you can have them cover the rest for a certain amount of time.

That's exactly what my employee proposed.