Cash out refinance, rent out, then move from primary residence - or Sell and move?

[Byron Slaybaugh]

Hey all - new to BRRRR community and looking for some help here. My wife and I are getting our house in Austin ready to sell. We have a great deal of equity in the house and have completely renovated it while living here the past few years. In talking with our agent about listing prices, our equity currently sits at around 240k. Am I way off base in thinking about doing a cash out refinance instead of selling and then rent it out? Ran the numbers on the BRRRR calculator but I feel like something is off on my end. Says we would be negative -350/mo but if we do a cash out refi, we would lower our mortgage 1k per month (currently have a 15yr fixed). What am I missing? Looking to rent out the house in Austin for positive cash flow and then take the rest of the cash out refi to put on a new home in another state. Thoughts? Am I off base here, should we just sell? Thanks!

-Byron