I would say that with younger students, solfege is more helpful than theory, unless they have already been studying theory. And after solfege, interpretive analysis, such as voice leading, and one thing that combines solfege and some of theory and voice leading is figured bass. Any piece where you can make figured bass notation, if you know how that works, can help you really memorize the bass and harmony. If you don’t know how it works, you simply write in under the left hand the intervals above the bass note in numbers. What is neat about this is that rather than thinking about the pitches, you are thinking about the intervals, which is how you reach and place notes, and is a whole other way to think about the notes. It emphasizes their relationships more, which is more musical than pitches alone. So if you take Salzedo’s Gavotte, for example from the Suite of Eight Dances, the first measure of the left hand in figured bass would be 10-5 (or 6-5 if you measure note-to-note), and you could call the d and c 5 and 4. It would be particularly useful in the Menuet. You could do this in the right hand as well, come to think of it, by measuring down from the top note, or up from the bottom.
Figured bass basically means you numerically list the notes above the bass line. In baroque music you will see this written as 6 5 7 and if the bass note is c, the upper notes are a, g, b. The third is assumed to be there and so you rarely see the number 3.