Financing Strategies for Downsizing?

What is the best way to go about financing when downsizing? I wouldn't be doing this for at least 3-5 years, so it's just a hypothetical at this point. We currently have a $475k house with about $95k left on the mortgage. If all goes well (no layoffs at work or large repairs which go beyond our budget), we'll have the house paid off in a little over a year, and would have a decent savings (~$100k) built up about a year and a half after that. (There are a lot of ifs in that scenario, of course).

Assuming we are able to get the house paid off as planned, what is the best way to go about financing a move and working out the timing? Ideally, I would like to be choosy about our new place, AND of course get the most that we can out of this place. The options which Google gives are:

1. Home Equity Loan

Use that to buy a house, and put this one on the market as soon as we close. The downside to that is I could see this house sitting on the market for a while since it's in a high price range for our area – and every month it sits on the market we would loose $900 in taxes + home owner's insurance, plus whatever interest we're paying on the home equity loan.

1. Cash Out Refinance

I can't say that I understand the difference between this and option #1.

1. Bridge Loan

I don't know of anyone who offers these, but apparently they're a thing.

1. Sell First, Buy Later

My wife would hate this option, and with us having kids, I would likely hate it too. It would allow us to not take out a loan, but we would still have to sign a lease for a rental. Finding a short term lease would likely be difficult. And moving twice would not be fun.

Is there anyone who has experience with this, how did you go about it? When we bought this house, we had a large savings – but if we were to sell it, we would have much less savings this time around because it is all sitting in home equity.

And yeah – we just moved so maybe this is buyer's remorse and I'll get over it. But it doesn't hurt to start researching now…