Starting in the middle of the Rhine on a KD Cruise

Welcome to the forum.

Since the cruise is important to you, it's important to tell you that it's much better to cruise more of the river than your plans call for. Bacharach-St. Goar is good, but Bingen-St. Goar is twice as long and twice as good. Here is a map of that scenic part:

https://gruppentouristik.com/sites/default/files/anbieter%202/Bingen-R%C3%BCdesheimer%20F%C3%A4hr-%20und%20Schiffahrtsgesellschaft/Rheinlauf.jpg

Also, starting in St. Goar means some wasted time - the boat chugs hard but slowly against the river current as it travels south - you will have to spend 2 hrs 40 minutes on the boat in that direction, instead of 1 hr 25 (Bingen-St. Goar, with the current.)

So... What you might do is take the train from FRA to Bingen station, hop off the train, and walk to the KD dock - it's just a few minutes. Have lunch at a riverfront establishment and then cruise (14:30) north to St. Goar (15:55.)

OR, you can take the train to St. Goar, check in, then catch the train south to Bingen whenever... besides the 14:30 boat there's a 16:30 boat as well.

You don't need to pre-purchase tickets. You'll pay €16 for Bingen-St. Goar each after your 20% discount for arriving in Bingen by train (show your train ticket at the KD kiosk.)

What are your plans for ticketing yourselves from FRA to St. Goar? There is a way to ticket your trains so that it costs you no extra money to return to Bingen if you do the check-in-first-in-St. Goar option.

We have not heard about the K-D boats filling up on any normal basis. They're large and don't have reserved seating.

... then we hope to take a ferry down the Rhine to Bacharach.

It is important to understand that although St. Goar to Bacharach is down on a normal map, it's actually UP the river, as in against the current. The current on the Rhein is very strong, so going against the current means an extra 50% in time. Unless you really like sitting on a boat looking at the same scenery for a long time, take the boat down the river, as in from Bingen to Bacharach to St. Goar.

There is a ferry at St. Goar, but it goes across the river to St. Goarshausen. The vessels that goes from St. Goar to Bacharach are referred to as "ships".

This is such a short ride going from St. Goar to Bacharach it is barely worth it. Do take the train farther south and then ride the ship back up to St. Goar. Otherwise you miss the major part of the Rhine and all of the castles.
The boats never fill up, especially in the afternoon. You don't have to worry about getting a ticket.

We did Bacharach to Boppard a few days ago on the Goethe (K-D) and had no problems getting tickets.

https://goo.gl/photos/S1nk2MddEoZF7JgYA

I have never heard of the ships filling up. The seats are not reservable. First Class on the ship will have fewer people competing for the seats. I've always just visited the ticket office next to the dock, and in Bacharach I like to have a bratwurst cooked in the little hut next to the dock parking lot.