What if LA cancels the deal with Minnesota and just gives the Sox Maeda instead of Graterol? Maeda's not exciting, I know, but he's an average-ish pitcher without major health issues (at least, I can't find any evidence of any), wrapped up for the next four years at a price so low that if he tanks they can DFA him without worrying about it. He is a plug-in replacement for Price in much the same way Verdugo is for Betts -- not as good, but good enough to contribute, and much cheaper.
Obviously, getting a high-upside prospect would be better, but in terms of continuing to contend this year, this would have its advantages.
EDIT: This is assuming it's possible for a team to back out of a deal with another team based on a 3rd team's balking at the medicals. Not sure how the rules work there.