We recently had a snafu ourselves - turning on/off certain objects kicked off new reports, broke some others - all of which caused the system to hang, max out on heap memory, and then ultimately reset several times. We wound up having to fix on the dev side, push back to stage to fix that, and then stage would act right so we could continue our monthly copies.
Our TAM had us install a "PreCalc Analyzer" in our stage environment, which is cool. It's its own project and pulls in details from the other environments and lets you see the 'trouble-makers'. Kind of like task manager in windows... Was able to quickly point out certain reports that were taking several hours to calc through. If you don't have that, definitely ck into it.
One suggestion I have for Apptio (maybe this is an enhancement type request I need to enter?) is if there was a list of the OOTB reports and what objects they were connected to - that may exist, but we haven't seen anything. Not having that is making us go through and catalog each report to pull those details together manually. Then we can quickly check if we need to add/remove objects and see what potential impacts we may have on the reporting surface.
BTW, deleting unused OOTB reports didn't work in our experience - since OOTB, they're hard-coded in somehow, so they just pop back up. In those cases, I just deselected the pre-calc button and hit save.