My questions are: Does offering $375k to break even but cash in on equity make sense?

I actually prefer these systems because there’s no cash/check to deposit at the bank.

It's tougher to get cash flow upon move out these days but if you're patient, willing to do some work, or live in lower cost/fringe areas you can make it happen or at minimum put a serious dent in your housing expense which is still a win in my opinion compared to renting or buying just a primary home.Also if you're a bit short on cash, make getting a seller credit part of your financing strategy.

Ultimately, the goal is to add the property to your rental portfolio for consistent cash flow.

The cost of entry is low while the cash flow is high.

So one market might be a great cash flow market.

The MIL has owned the property for 4 years and there is no mortgage (purchased in cash by her grandson; I raise this to you in case there are capital gains implications for MIL and DIL when the latter sells). 

During rehab process the bank sees us with; 2 mortgages, 0 rents, and 1 income (spouse not working) and would be too risky. 2 mortgages will make us at borderline break even cash flow with existing income.

Looking for cash flowing single family homes in the Portland, Beaverton, Newberg, Salem areas of Oregon.

I will live in the home for 1 year and then reevaluate whether to make it a cash flowing rental or simply flip it.