Sorry, Spy, none of this makes much sense. If they "need" a long guy, which nobody carries any more, give Jax the starts and make Shoemaker the long guy. But worrying about that is pointless anyway.
If Maeda makes his rehab start, he's not taking Shoemaker's next start.
It's not a matter of 3.5 or 3.75 months...it's a matter of not wasting starts on a one year FA who isn't any good, in a lost season.
There is no reason to have Shoemaker on this team. None.