At this point I would keep Doolittle, Rodney, Guerra, Rainey, and Suero. Maybe Sipp, depending on how well he does against lefties from now until the deadline. So I need at least two relievers, preferably high leverage guys.
I wouldn't move Keiboom for any relieve or any combination of relievers. The only way I move Keiboom is for a significant piece or pieces. So like Stroman and Giles, and then I work out a deal where I flip Stroman to the Yankees for Kanhle, Florial, and [insert pitching prospect(s) here]. Then I'd flip Giles to someone like Minnesota for some prospects and use those prospects to get another reliever (like Smith). So a potential trade would look like this:
Keiboom and Joe Ross to the Blue Jays for Marcus Stroman and Ken Giles
Stroman to the Yankees for Tommy Kanhle or Chad Green, Estevan Florial, and Jonathan Loaisiga or Albert Abreu.
Flip Ken Giles to the Twins or Cardinals for Luis Rijo or Blake Enloy and Akil Baddo/Griffin Roberts and Dylan Carlson
Trade Luis Garcia, Enloy/Roberts, and Luis Garcia and another piece for Will Smith
But I'm certainly not parting with him for rentals. And there are too many teams still "in it" for it to become a buyers' market. So whoever gets traded is either going to cost a lot of money or significant prospect value.