Considering your pack-it-all-in plans, David has provided you with a reasonable train schedule for your day. It puts you on high-speed trains between Basel and Mainz (IC, ICE) and you get to Bingen at 12:09 for lunch prior to your 14:30 cruise.
The QdL ticket day pass can be a good value for some trips, but using it would mean a very delayed arrival in Bingen Rhein Hbf at 15:56 since you must use the slow trains with this day pass and since you must leave after 9 am.
"I'm also unfamiliar with the Sparpreis? Where can I find info/purchase?"
Information: https://www.bahn.com/en/view/offers/germany/saver-fare.shtml
Purchase is done from the DB itinerary page; enter your data and search: http://reiseauskunft.bahn.de/bin/query.exe/en
I just searched David's schedule for Basel-Cologne on Set. 11 and found a price of €139.80 for two at DB. You can find it too if you enter two stopovers - enter a 2-hour stopover in Bingen and a second 2-hour stopover in St. Goar. (Note that your ticket includes a train segment between Bingen and st. Goar that you are not using because of the cruise, but that's OK.)
A second option appears as well, priced at only €79.80. Leave Basel at 9:13, arrive Bingen Rhein Hbf at 13:34; take your 14:30 cruise, do Rheinfels, etc. and you still reach Cologne at 20:02.
Either plan works depending on your preferences but... What about your luggage? You have two potential luggage problems, one in Bingen and one in St. Goar...
Bingen: If you are packing the way Rick Steves tells you to pack, it is possible to use either schedule above and walk between Bingen Rhein Hbf and the KD dock for your cruise. If you can't walk for 15 minutes with your bags, you will need a taxi, or you will need to do as Lee suggests and use the Bingen Rhein Stadt station instead (which involves a shorter and less complicated walk.) You can use the Stadt station with either the 8:13 departure from Basel or the 9:13. With the 8:13, just get off the train at the Stadt station at 12:01 (instead of 12:09 at the Hbf station.) With the 9:13 schedule, get off at the Stadt station at 13:31 (instead of the Hbf station at 13:34.)
St. Goar: You probably don't want to hike up the hill to Rheinfels with your bags. There are no lockers at the station but the TI office will hold your bags for you. See their hours here:
https://www.st-goar.de/18-1-tourist-info.html
IMO your itinerary for this day is overpacked with travle and misguided. I would spend the night either in Bingen (drop bags at hotel there, and cruise bag-free) or in St. Goar right after the cruise. Then continue your journey the following day to A'dam, making a stopover in Cologne on the way (Cologne station has a baggage storage system which makes this simpler.) St. Goar is a lovely town with the most scenic setting on the Rhine. Love that view across the river.
https://farm4.staticflickr.com/3734/8921199351_dc4bb7f642_o.jpg