The monthly payments are great, but the issue I am running into is what to do with idle cash.

Without any cash it is unlikely unless you can find a 100% seller financed deal (they do exist, I just did one a few months ago).

How did you achieve this type of cash flow?

Talk about CASH FLOW!!  

Retaining your current home at a 2.875% mortgage rate maximizes cash flow, while accessing $65K in equity provides liquidity for your next steps.

So if you are anticipating higher rents and therefore higher income next year you may want to wait till then if you are trying to maximize the amount of the cash out refi.

The cash on cash return is only meaningful when you evaluate it based on your long term plans.

Start by analyzing cash flow and market demand for each property to decide which one to rent out.

I used both and now own the property free and clear. 

Highly recommend you looking into a checkbook IRA instead of cashing out.Sure you can take out the principle since you’ve already paid taxes on it but this money is supposed to be for your retirement and in a Roth your real estate can grow tax free, though check with a CPA to see if STR will trigger UBIT in an IRA.