I think this is about all that the executive can do within the bounds of separation of powers. I think Biden needs to be quite frank and give the moderate and left-of-moderate America some tough love on this one: The only way to turn this around is to show up and vote
consistently, and that it won't be quick, and it won't be easy. The GOP has been building up to this for decades and managed it essentially against the will of the majority of Americans. This needs to be a wake up call - the fact that something like that can happen in a nation that identifies itself as a democratically-elected republic means that something
isn't right. The balance of representation has been perverted to reward a minority of citizens at the expense of everyone else.
The real inherent problem -the critical design flaw- with the United States is that our foundation was
compromised while it was being built - the Senate shouldn't even exist (as it does) in a republic, it doesn't represent people, it represents arbitrarily-drawn land - and somehow that land gets to decide who is on the Supreme Court. You cannot defend it with reason. I'll tell you how unreasonable the Senate is - California could decide to chop itself up into each of its constituent counties. There are 58 of them. This would more than double the size of the Senate and give the West coast a super majority in the senate, all for meaningless, invisible cartographic boundaries. Or Texas could turn itself into 254 states. I mean why not? That might sound absurd, but it's no more absurd than the arbitrarily drawn rectangular shapes in the center of the country having 2 senators each.
Who wants to help me start a movement to enact the original
Virginia Plan for the Senate?
It would still be problematic due to gerrymandering, but at least it would be
representational. I'd be curious to see how the nominating part would play out.