I notice I can likely do a cash out of $100k+ at either my current rate of 2.75% or maybe even 2.625%. The goal would to be maximize the "conforming loan" limit, and then I would be free to pursue lower interest rates exclusively for a few years. But I would probably restrain any future refinances to the greater of 70% and the conforming limit unless something amazing popped up. I ran it by the wife, who says "I don't know much about investing. Did you ask that mustache?" Consider yourselves asked :).
The money would probably go to 60% VEA 40% VWALX*, giving a total taxable split 1/3 RZV, 1/3 VEA, 1/3 VWALX. Doing my best to backtest that allocation, it gives a pleasant combo of better returns than all but a 100% VTI stock allocation, but better worse case scenarios that most "guru" allocations. Also, a mixture of VEA and VWALX distributes a yield of about 2.625%, similar to the mortgage rate. Monthly mortgage payments are higher because of principal, but the investments (stocks anyhow) are likely to grow dividends over time.
Of course we could just try for a rate reduction. Nothing wrong with a lower monthly payment by a few dozen dollars either.
*unless I try to get a $500 brokerage bonus from etrade or somewhere.