Even though you may be able to get a slightly better interest rate at a bank, by time you pay for the appraisals and costs you will almost certainly be in almost the same position financially and have a far more flexible mortgagee. 

Requirements: 2bed/1bath minimum for our family. 3/2 ideal, but we're flexible for the right place.

Because it is a family member buying the home you have some flexibility with the timeline and I would reconsider the 1031 because the timing of it seems to be the hardest part.

Your local lenders often have some flexibility in their loans, but often times be recourse.  

I am looking for recommendations of credit unions or banks, either in Connecticut or National, that is flexible in terms and mortgage products offered.

But, they have a flexible, albeit busy, schedule. 

I will be eligible for a physician loan for up to a) 750k-850k mortgage with 0% down, no PMI  b) 1.25m with 5% down payment, no PMIc) 1.5m with flexible down-payment, no PMI.Of course if I move anywhere else in the country the numbers make more financial sense as the bay area is currently probably the most expensive housing market.

Does anyone have any recommendations for more creative/flexible mortgage lenders?

Depending on your flexibility on location you can find a place that will cash flow (at least once you move out of your owner-occupied unit).  

I have a lot of flexibility in how I can file.