The best strategy isn't to try to neccesarily change the perception of the incumbent but rather make an affirmative case for the challenger. Basically, "I like Tester, but this Tim Sheehy guy is also cool and he is a Republican so why not"? If people have a positive view of both candidates, ceteris paribus they are going to vote for the R in the double digit Trump state(s).
Except it's not ceteris paribus. It might be if it were an open race. As it is, Tester is a three-term incumbent who sits on Senate committees that are relevant to MT's interests. That's an advantage Tester has that shouldn't be understated.
Otherwise, I agree with the points you made. It's exactly how Byron Dorgan would've been beaten by John Hoeven in 2010 ND-SEN had he bothered to run for reelection.