All of that? Done. The GOP does not care what it looks like in the pubic eye but, more narrowly, only cares what it looks like in the eyes of their benighted supporters who still believe the election was stolen and the 1/6 insurrection was a mix of tourists and ANTIFA.
If you make good faith public efforts at bipartisanship,, show you are willing to negotiate, willing to not get everything you want,
Do that up front for all to see, then if one side (repubs) still obstruct and make party line decisions, it will only make them look bad in the public eye...
Then, after those good faith efforts are exhausted....You have the moral high ground to move forward and show leadership in the face of gridlock....