I was already setting aside the $140 to build a cushion for repairs or updates.

So with the refinance, I get a good cushion to start saving for the next rental property purchase plus a new cash flow of $436. 

Hi Mary,That's great you have a nice cushion of savings available.  

How is a good way pick this place up with minimal money out of my pocket instead of putting the 50k down since I'd have an automatic  ~40k cushion built in?

It lowers the amount of income you need to replace and it helps you build up a cushion if things don't go smoothly in the beginning.

It definitely requires more time and effort if you're delegating the responsibilities to yourself. 65k would really open a lot of doors in terms of houses prices, with 25% down you can purchase at least up to 260k with some cushion in case something goes wrong or if you need the money for emergency use. 120k-170k is the sweet spot where you can save money managing while reducing a major repair that might come up as well as effectively maximizing returns.

Any sale proceeds would go a long way towards adding a cushion towards our flipping endeavor and/or allowing us to take on a bigger project. 

As long as you have cushion to replace if necessary, maybe just roll the dice.

Same author, Nassim Nicholas TalebHaving a cushion or multiple ways to win helps reduce the damage when the error happens. 30% equity when you buy implies that a correction is not as likely to hurt your overall position.

Your cushion of a security deposit gives you one month of leeway and of course you still have to consider cleanup of property before renting.