A waltz in sonata form can work.
Often the 2 chords will be an inversion apart, but when the right hand gets into the bass clef, the chords are sometimes the same. The Root is usually at least a fifth down from the first chord, but particularly with the F major chord, I find that I can only do that when the melody goes up high. If it stays in the first octave, I have to have the first F major chord be in first inversion, a third up from the root. The hardest part I have found so far about composing this piece is having the rhythm of the Waltz and the form of the Sonata, while keeping the piece coherent.
Will the bass stay the same throughout the entire piece? That's asking for bored players and audiences unless you can work a miracle with the right hand. I strongly suggest you have some variety. Also, why is there a problem with combining rhythm with form? If I asked you to write any other piece in sonata form, you would manage fine. Why is the waltz different?
Please try not to make your piece sound blocky as is often the case with rigorous planning and a clear form. I'm glad that this time, you haven't written e.g:
Measure 16-17: Second closing phrase which will move from ii to IV with a staccato bass line and some arpeggiated right-hand notes.
That can make your piece sound rigid.
I'll answer that with another question: what do you think of your idea of combining the rhythm of the Waltz with the form of the Sonata? Constantly asking us for advice is hindering your own creative process. If we had said we disliked this idea, I am fairly sure you would respond defending it (if at all.) Don't be afraid to try new things.