It's tricky since there isn't a concrete deadline (there are a couple factors that play into it) but I think July 3rd is safe. However, I don't think it matters nor is the reason. raBBit pointed out that there is doubleheader that day.
Right you'd still pretty much have to sign Cole. Roll with Cole, Giolito, Cease, Kopech*, Quintana.
*If he needs to go to the minors to start the year, then Lopez I suppose.
At this point, I don't even care if he plays RF. Just take him out late in the game and DH or sit him when Giolito or anyone else with future promise on this team starts.
I think most people know he is nothing though. Just would rather see him in the lineup instead of Alonso. Now, when Beef comes back, he should go since Collins and Abreu should split 1B and DH.
Doing some thinking about it, I'm fine with him in RF. The entire rotation outside of 1, arguably 2 guys, is important going forward. Go with a better defensive team when Giolito (and Lopez) is on the mound.