The same sort of creative process going on in so many venues, FR included, about how the Senate might force the issue, faced with a House that is procedurally derelict on a matter that has interbranch ramifications.
I totally agree with you that POTUS can plead to the senate. That is the correct venue, not SCOTUS. I'm sure there is substantial precedent for communications from the Executive. Maybe Trump can use the constitutional power of ordering Congress into session, and give them his impeachment as the subject matter. I'm ignorant of instances when this particular constitutional power was ever exercised.
Whitewater Independent Counsel, Robert Ray, brought up an interesting possibility on Laura Ingraham last night. He pointed out that a (Whig?) House censured Andrew Jackson (not 'Johnson') and the Senate confirmed, but the subsequent Dem Congress - both bodies - overturned the censure which apparently nullified the record.
Of course the pathological Dems will claim through to Armageddon that Trump is impeached, but this presents one possibility of expunging the gross partisan impeachment stain for history.
I would like to see SCOTUS throw out the Articles of Impeachment on numerous unconstitutional grounds thus settling the issue conclusively and inarguably historically; that would dampen Dem fervor for more attempts to impeach and other silly shenanigans... but I suppose any port in a storm. :-/