Borucki
Gotta keep the lefties AMR
Bolsinger, Valdez, Harrell, and any other AAA pitcher will likely be on the top of the list. It'll likely be a committee thing with anyone on the 40 man roster. Biagini may even get more reps.
It's not like it really matters. The rest of the year should be an audition. You never know what you could have out of any of them, even if they have sucked thus far. Although I am sure they will try to keep the team semi-competitive. It ain't going to be the Leafs Circa end of 2015-2016 season or anything.