As georgi said, knowing the frame will be (and actually always is) very important. Being able to get the mic even just 1 foot closer will be a noticeable improvement.
As for sound blankets/baffles, it depends on the space. If it's huge and open, then putting up baffles and keeping them out of shot might be too much effort for minimal gains. One thing you could try is having some sound blankets on C-stands, and putting them up in front of the surface that'll reflect the most sound to the front of your pickup pattern. So, basically, ignore surfaces that are off mic. This will still involve a lot of dicking around between set ups, so it's up to you to determine if it's worthwhile or not. Maybe you can arrange a visit to the location to record a few tests?
Mic wise, i'd suggest going with the Schoeps because it's a shotgun. This is a bit beyond my level of experience on set, but i believe a shotgun would be better than a hypercardioid in a large, reflective interior. Also, it would be fantastic if you could get a hold of some radio mics. I know we all like the perspective given by booms, but radio mics will give your sound post people more choices. And choices are good.
Finally, do your best to get hold of a script marked up with which slate covers what. Like this one. I love it when i get these, because when i'm looking for alts, i can see which lines are in which slate. Depending on how consistent the performances are, maybe your dialogue editor can use lines from the CUs for the wide shots (which will have more reflections). Where i'm from, it's usually continuity (aka script supervisor) who'll have these, so if you're on a low budget skeleton crew, it might not be feasible.
Also, bring some balloons or a cap gun so you can record IRs for each set up. They'll be super handy for foley and ADR.
Hope that helps!