There are actually several viable options here. I am assuming that you want more than just "emergency" care, which, as Greg already indicated, is provided by law anywhere in the USA (of course, they can still bill you for it — it's not actually "free").
1. ACA plans. No need to use (expensive) COBRA any more — quitting your job is considered a "life event" that entitles you to get a brand new ACA plan. No pre-existing conditions, no underwriting, BUT you will be best served by plans that have a large, multi-state network, esp. in the states you'll be passing through. [This will probably mean that you'll need to avoid HMOs, which generally restrict you to coverage in one geographical area, with zero coverage outside that region. You'll do best with a large PPO network, whether through an HSA, or alone.]
2. Travel health insurance. Depending on how long you'll be away, you may be able to keep your regular HMO, but buy a travel policy to supplement it for the time you'll be away. Again, be sure to check the size of the network of Dr.s/hosp./etc. before you purchase. Often, these policies also provide transportation back to your home region. Pre-existing conditions are excluded from coverage.
3. Temporary insurance. Similar benefits to travel insurance, but no transportation option. Again, look at the network carefully. The network is everything! Pre-existing conditions are excluded from coverage.