You need to be a resident of the state to use the exchange. To be eligible for premium assistance your MAGI must be less than 400% of the FPL and the MAGI includes income excluded under FEIE. As long as you meet these requirements there is no reason not to do what you suggest.Wonder if there is an option to use a US address and just pay the premiums even if outside the country .
With subsidies low income premiums may only be a few hundred dollars a year.