Here are two items to consider when these situations arise.
1. When you list your home for sale many loan programs will limited the amount of cash out you can receive within certain time frames from when you listed the home for sale so make sure to check with your loan officer or lender to see if you do not sell the home and then come back to refinance how that would impact a potential refinance.
2. Be aware of occupancy requirements on the loan you are requesting if you are refinancing your primary home most times you will be required to sign an occupancy disclosure/agreement/affidavit so make sure if you do plan on buying another primary in the future it does not contradict/conflict with or violate the occupancy agreement/disclosure/affidavit that you sign when you refinance.
So as you can see with either approach there are potential time constraints that will impact your decision.
There are other alternatives that may allow you to buy a new primary home now and not need to refinance your existing home while still avoiding the mortgage insurance on the loan which is why I imagine you want to take out the 20% to begin with.
I am located in 33015 which is in or near your area, give me a call or let me know and we can arrange a time to meet in my office to discuss your situation and options in more detail.
There is NO COST or obligation for the consultation.