Here is a list of what we ended up doing - and thanks to everyone for the very helpful advise.
The concierge gave us the best train information and routing, and it worked out fairly well with a little stress along the way because we left later than planned - but we arrived Kawaguchiko at 11:27am along with hundreds of new friends who crammed into train, standing room only.
Upon arrival, we stopped at the tourist info counter and a really helpful and friendly attendant planned the balance of our day based on the traffic conditions...apparently we were not the only people with this plan in mind. We walked over to Toyota Rent A Car and signed out a cute little Aqua Prius, and off we went. Driving right hand drive was not as challenging as I feared, and within a few minutes I was perfectly fine.
Traffic was pretty bad - it took about an hour to get to the festival, and we stayed for around 90 minutes. From there, we back tracked to both the wind cave and ice cave - both were highly underwhelming and I would not recommend them, and with the traffic on the return, it took time to get there as well.
From there we decided to try for the 5th Station, although the toll gate attendant who didn't speak a word of English tried to explain that we had to be off the road by 7P - but we had time and other cars were behind us, so up we went.
The view from the top was amazing, not just of the mountain, but of the valley below, especially as the sun began to set. We headed back down without feeling bad for missing a couple other stops. With an uncertain train schedule and needing to go back to hotel #1 to get our bags and move to hotel #2, we decided to drive back to Tokyo and keep the car overnight, then drive to Hakone earlier in the morning to avoid the crowded trains. We though this plan would save money, until we encountered the tolls - and lots and lots of tolls.
The next day we drove to Hakone, returned the car, visited the Onsen and spent the rest of the day going from the railroad to incline train to ropeway and back - it took the balance of the day but was worth every minute.