First, I'd start with the basics... have you done a maintenance run for index rebuilds and statistics updates? Your messing with maxdop allows queries to recompile. Something may be off in those. Besides, it's just a good habit.

Next, VM is... touchy. You need to get into the VM monitoring/assignment software and make sure your resources aren't being reassigned or disabled during slow times and then not reallocating during higher peak times.

My personal recommendation is do a maintenance run on the database, then check your system for the long running queries by looking in sysprocesses for them. Spot check the execution plans for those particular procs. If nothing is obvious in them, get your hands on the VM software and head for a forum you can ask explicit questions about that VM on. It could be anything from your VM not having RAW storage and thus the CPU has to decompress/translate to simply having throttles activated in the VM software.

Troubleshooting VM from a forum is painful at best, particularly without a lot of experience with it (which I don't have) and access to that particular VM software (which I also don't have).