Ralphie,
Thanks for the detailed post. There's a lot to unpack here. As an experienced owner of a real estate brokerage, a property management company, flipper, investment property owner and active stock trader, these are some of my thoughts:
You don't need 20% down to purchase a home. With an FHA loan you are able to put down as little as 3.5% down and finance the rest. But you do need employment income. No traditional lender I know will offer FHA or other type of financing if there is no employment income local to where you are buying (unless it's remote work). Even an offer letter for a job you're about to relocate to TN or elsewhere may work. That may be the first order of business for you to consider.
When considering whether to sell vs. rent out a property, my general advice is to consider the rental income the property would provide (and equity gains as the property continues to increase in value), and determine whether your use of proceeds from selling it would give you a better return on investment. In other words, if you've got a better opportunity for that money, then sell it and pursue the better opportunity. But if not, your property is a highly lucrative source of income and wealth building. I often compare it to the Aesop Fable of The Golden Goose. If it lays a golden egg for you each month, don't sell it--unless you have a better use for that money.
Some options you may want to consider: if selling your home in Martinez, CA allows you to pay cash for something in TN then you wouldn't need to worry about a job in order to get a mortgage loan. While you'd have a smaller sum left over if you paid cash, it would give you some breathing room/time to re enter the workforce. Once you do, you could refinance to pull some of that money back out (though generally, if you don't need it and don't have a compelling reason for it, might as well remain a proud 'real' homeowner).
I know this is off topic, but COVID restrictions seem to be rapidly winding down nearly everywhere, even in the Bay Area. Would the gym bounce back and recover if you held on just a bit longer?
Lastly, I've helped a number of people relocate out of California. I don't know if you've already done this or not, but I'd strongly recommend you take at least a couple of trips out to the Nashville area and spend at least a few days there, if not a week or more, to get a feel for the area. Not as a tourist, but as though you were a local. Spend time talking to people. Get a sense for the demographics, the attitudes, the politics, the beliefs, etc. I say that because there are few places that are a bigger contrast than the Bay Area and Nashville. It might be the perfect thing for you! But you may feel like a fish out of water. There's only so much of a feel for a place you can get without spending some time there in person. The more in-person time you spend there before uprooting your family and buying a house there, the less likely you are to later regret it.
Hopefully this gives you some good food for thought. I'm happy to engage further if you'd like.
Aaron Lewis