BTW is 2/3rds structurally out of reach for R's in the House or not?
There's a plausible scenario where Senate R's could get there (2022 midterm blowout, then D's barely hold onto the presidency in 2024 because Trump while R's win everything competitive downballot, then another midterm blowout in 2026).
In the scenario you are describing I don't think such a majority would be 'structurally' out of reach, but that's a pretty outlandish scenario. I think ~250-260 is likely the realistic seat ceiling in the current politcal climate for Rs (D ceiling is about the same though maybe slightly higher).
2/3 would require 290 seats, which is far enough out that I'd call it 'impossible'. It'd probably require Rs winning every district that Biden won by less than 10, more or less, which would be a crazy swing. I don't think every race downballot is suddenly going to become Mcauliffe vs. Youngkin.
To get to 290, Republicans would pretty much need to win every district Biden won by 20 or less. Winning everything he won by 10 or less in only gets them to high 240s.
OK, so it's a much harder lift than the Senate (there are only 15 states that voted left of VA in 2020 and R's already hold one senate seat among them).