You are being paid for your non-flying work with free flight time. You are not being compensated for flying. It's compensation for flying that the FAA is trying to regulate.
Be careful. FAA could just as easily consider the OP to be acting as a corporate pilot, which requires a commercial license. Trying to separate his normal duties from flying might well be problematic in court. There are several good posts above regarding "free flight time" as compensation. I think one would have to survey historic cases and see how the FAA was applying - and reacting to - these various situations to get a "correct" answer here. For the specific (and long moot, I'm sure) case above, it's hardly worth the effort.
AOPA and ALPA both have lists of aviation attorneys that could check on this. With all respect to everyone, don't rely on legal advice from here! :D