The right chart shows the median $/SF for properties sold that conformed to our property profile.

To get that high, I will have to put down 235k in order to bring the loan amount to conforming limits (765k). 

It’s pretty tough to impossible to purchase with a mortgage because the quick closing time and you don’t know if the property will even qualify (conforming loans require a “functional”) or appraise for the loan.

As an aside, this is always the issue with non conforming apartments that aren't set up the right way.

Although, there are overlays, exemptions, variances, legal non-conforming, and grandfathered properties in nearly every municipality.

I think the HML will also give you greater flexibility in what you purchase since you won't be constrained by a conforming loan (which should strengthen your offer). 

I recently graduated from college and have a limited work history that makes it more difficult for me to "check the boxes" needed to conform to Fannie/Freddie loan requirements.

She might be able to help, or may have a colleague who can find a way to originate the loan.What about a local bank that wouldn’t have to do a conforming loan?

Don’t go to the big banks, try small local banks in your area.i don't think commercial is more flexible if you have no history, especially if you are buying a single family residence, as even a commercial loan will have to conform to  ability to pay rules for consumers if the property is a SFR.

However, FHA loans, as any other conforming loans, are for residential property purchases.