Cz makes a 223 bolt gun that could be rebarrelled. Not sure if that would meet your definition of cheap though. Not sure it is doable but you could rebore the barrel to 300 blackout. Not sure if the dimensions would work but could be worth looking into.
Are you bringing this up because you're just learning this and think everyone else is, too? Browning offered left-handed rifles with 0.378" bolt faces, Ruger offered left-handed rifles with 0.378" bolt faces, Tikka offers left-handed rifles with 0.378" bolt faces, Remington occasionally offers left-handed rifles with 0.378" bolt faces, Zastava offered left-handed rifles with 0.378" bolt faces, Savage offers left-handed rifles with 0.378" bolt faces, Kimber of Oregon offered left-handed rifles with 0.378" bolt faces, ad nauseum. And so did/does CZ. Everyone (except you) knows that. And your point was what? They can all be potentially re-barreled or re-bored.
The cheapest option would be to locate a left-handed Ruger American in .223 and a right-handed Ruger American in .300 Blackout, swap the barrels, and resell the right-handed gun to recoup some cash. The next cheapest route would be to re-barrel a Savage or Ruger American with a pre-fit barrel. The costs only go up from there.
