1) Can I buy a ticket that let's me get off at any particular village, explore, then get back on one of the next boats and continue on, maybe two or three times before reaching my destination?
Yes - the KDRhine pass sold by a "middle man" vendor for €32 - but don't do it. A Bingen - St. Goar cruise with the train-ticket discount costs half that, to Boppard only a little more.
2) We will have our large backpacks and small bags with us, so I'm not sure if there's a way of storing or managing the luggage?
St. Goar's tourist info office will hold bags. But their lunch breaks and closing hours may not suit you. There are no lockers in these towns. For this reason, your plan definitely deserves an alternative Plan B.
"I think I'll be taking a train to Bernkastel Kues (Wittlich Hbf) and will skip Koblenz."
Couple things... Wittlich is a different town from Bernastel-Kues (which has no station - you bus to Berrnkastel from Wittlich station.) Also, you are skipping a lot more on the Rhine (and Mosel) than Koblenz. You'll have time for Bacharach and St. Goar's Rheinfels Castle (an interesting set of castle ruins, with a museum,) but it very much seems a shame that you are skipping all these other places on your sprint to Bernkastel...
Two completely intact medieval castles from the Middle Ages...
Marksburg Castle
Burg Eltz Castle
Boppard
Cochem
Perhaps your plan is to backtrack from Bernkastel to see these places, but Bernastel is well beyond these other places, and difficult to day trip from because of the bus - that seems pretty convoluted.
It's unclear to me how/when you will get to Bingen that morning.
One fix might be to book the NH Bingen (waterfront hotel) or other hotel for a night - drop your bags there in the morning for a bag-free cruise and exploration - then either cruise as planned with your stopovers in Bacharach and St. Goar, or just stay on the cruise boat to St. Goar... then hit Bacharach by train on your way back to your Bingen hotel.
Or... you could cruise from Bingen to St. Goar or Boppard with your bags, drop the bags at your hotel there, then use the trains to visit St. Goar and Bacharach. These towns are VERY close and easy to reach by train - 10 minutes between Boppard and St. Goar, 10 between St. Goar and Bacharach.