Update.
We ended up following Russ' plan which worked out in many ways but wasn't without it's hiccups.
We boarded the S8 for Mainz on time after easily getting my RMV Ticket, but of course the train was late so we missed the 8:03 to Bingen. There is, however, also an 8:33 which we discovered while at the station trying to figure out our options. This train would have still gotten us to Bingen with 10 or so minutes to catch the boat...but it was also late.
As the train pulls into Bingen, we see the boat pulling up to the dock...so we basically sprinted the 400m to get to the ticket window and she held the boat for us so we still made the boat we wanted.
Picking up the car early was a great option and worked out for the better because the car rental office contacted me to say that they needed to close early that day too.
After reaching St Goar, we were deciding how to best approach who all should go to fetch the car vs just letting them stay in St Goar with the bags.
Discovered the that tourist office WAS open and didn't have the odd hours for that Thursday like their site had mentioned (hours on google were correct). But I think they must have JUST changed the hours for the summer or something. They were very nice and helpful and happy to store our bags. They scoffed at the suggestion that we would need to pay for the service. Very grateful.
So we left the bags there, the family went to lunch in St Goar and I went to get the car. Now that it's only me, saved a bunch on further rail tickets and now that we had the car, we saved our legs/a few euro getting up the hill to the Berg now that we had a car.
Discovered while at the castle that Rick Steves himself had been there giving tours just 1 day prior. Would have fan-girled quite a bit had we been there at the same time.
We weren't able to take the time to visit any other towns along the way but took some time to visit Koblenz for dinner before we headed to Nurburg for the night.
Thanks for all the help everyone!