I think Vedugo's back issue is "concerning." Not clear what it is, but more than just a minor tweak:
From an article posted on MLB.com on 1/3/2020:
The Dodgers have been vague about Verdugo’s specific diagnosis, which has included lower back soreness and a right oblique strain. Manager Dave Roberts said Verdugo first felt back discomfort after playing on the artificial surface at Tropicana Field against the Rays in late May. He was batting .311 with an .869 OPS at the time, having replaced the injured Pollock in center field.
He continued to play through the discomfort, but his production dropped off noticeably from mid-July on, when he finished 11-for-53 (.208) with one home run and one RBI before going on the injured list on Aug. 6 with what was listed as a right oblique strain. After rehabbing in Arizona, Verdugo seemed to be nearing a return when he suffered a setback during a Minor League rehab assignment with Ogden.
I think the Red Sox would want to be particularly careful with the medicals on this before making Verdugo the centerpiece of the deal. Frankly, I was a little lukewarm on Verdugo before hearing about this, based on his high GB% and reported lack of lift in his swing, which limits his power potential (the Fangraphs scouting report from 2019 gives him a 50 FV, but also notes that he's probably mostly going to just have doubles power).
If they're not absolutely certain his back is ok, they either need a different main piece, or the other pieces need to be better. I still think they should be pushing for May as the main piece. But I think they at least need to get someone like Gray (or Gonsolin, if they think he can be a starter), especially if Price is going to LA.