What then is the possible (to stretch a point, knowing it wont happen) solution?
The Constitution must be amended to make impeachment possible. But of course many states are under Democratic political control, so even that is impossible.
I would favor a regime in which impeachment would be convicted not by senators but by governors, who by voting not to convict would be indicating that the conduct of which the POTUS is guilty is conduct they themselves, as executives on a smaller scale, might do. A Democratic governor might think twice about associating himself with executive lawlessness . . .
Such an amendment might also require a majority of both houses of Congress to go forward to the governors for an up-or-down vote (but, obviously, not be subject to presidential veto).
This would have been closer to the norm prior to the 17th amendment, when state legislators chose their Senators.
I think that the problem with impeachment today is that we have devolved from co-equal branches of government to unequal parties. It's no longer about the Congress against the President, or the House against the Senate; it's about Democrats vs. Republicans in every branch of government, with Democrats and the MSM having their thumbs on the scale of justice.
Senate loyalties are to the party, not the state, mostly due to the need to raise campaign funding every six years.
One would hope that a stronger allegience to the state by Senators MIGHT be enough to make impeachment and conviction more likely than it appears to be today, if only because Senators might fear for their jobs more likely if state legislatures appointed them.
-PJ
I believe the idea of an amendment for governors having the power to convict instead of the Senate is a reasonable one.
A governor of either party may feel a duty to cross party lines, as you say, to avoid associating himself with executive lawlessness.
It looks to me that the Founders made it very difficult to impeach and convict and may have not envisioned the politics and partiality that we are experiencing now.