Sounds like the car is definitely the way to go-- I was thinking there was some risk regarding the very few (nonstop) flights per day each way, if a flight got cancelled or severely delayed.
I'll be staying one night in Pune and then heading back to BOM the next night to catch a flight back home.

Given that I'm driving, I have one more question for those of you who are familiar with Mumbai. I'm going to have one day in Mumbai to myself (after landing from the US and before heading to Pune). I was thinking it would be nice to stay at the Taj Palace, as recommended by many on other threads on this site. Would that add a lot of driving time going to Pune over staying at an airport hotel like the Grand Hyatt? I know traffic in Mumbai can be a mess, but don't know if the time required to get to the highway is radically different between the two.