Oddly enough, the simplest approach I can think of is the one I have not seen mentioned at all.
Congress has set tax rates and made appropriations that are inconsistent with the debt ceiling. If Congress is stupid enough to pass inconsistent laws, the Executive gets to choose how to “faithfully execute the laws”.
So, I’d like to see the administration treat the debt ceiling as a nothing-burger. No coin trick. No reference to the constitution. Just blow it off.