So I have seen third movements of sonatas that are presto. But usually these are the rondo movements of 3 movement sonatas such as those by Haydn and Mozart. My piano sonata in A major that I am composing, I plan to have 4 movements in these forms and with these tempos and keys:

First Movement

Form: Sonata form

Key: A major

Tempo: Allegro

This is a generic Sonata form. One of many images I found of sonata form.

Now here is how I plan to have my sonata go for the first movement:

You can see that I have taken the introduction out. I felt that a slow introduction to a bouncy feeling sonata just did not seem right. And yes, to me A major feels bouncy. A fast introduction also did not seem fitting so I got rid of the introduction and just started with the first theme. Also, you can see I added repeats where the development and recapitulation are. I decided to have the first theme of the recapitulation be in the subdominant. It may be unconventional but it has worked before. I am questioning whether or not I want a coda to end the movement. I will decide once I get to the recapitulation whether I really want a coda or not.

Second Movement

Form: Theme and Variations

Key: D major

Tempo: Andante

I will have more than 4 variations and I also plan to have repeats for the theme and every variation. I have composed a nocturne where I basically did theme and variations with multiple themes. That was easy and it only took 3 days to compose it. If that is easy, than I can easily do 10 variations on a single theme, maybe even 30(though if I have 30 variations, it might as well be its own piece and not a movement of a sonata). Point is, Theme and variations, I find easier than sonata form in terms of composition. As for the feeling, to me D major feels majestic.

Third Movement

Form: Minuet and Trio

Key: E major

Tempo: Presto?

This is the movement I am questioning. I originally thought of having it at Moderato but I then thought "Since E major sounds like you have completed a major task, maybe I should have it at Presto." But this seems to violate the purpose of a minuet and trio. So should I have it at Presto and change the form or should I have it at Moderato and keep the form?

Fourth Movement

Form: Rondo

Key: A major

Tempo: Allegro or Presto(not sure which)

It would be more conventional to have this rondo movement be Presto. But I'm not sure that Presto fits well with A major's bouncy feeling. I do want it to be in the ABACABA pattern that is shown in the picture.

So I asked on other message boards about whether I could have the third movement be Presto and still be in that Minuet and Trio form and I got this answer:

While Presto is not too fast for the compound ternary form, since a Minuet and Trio is usually Allegro at its fastest, it would be better to call it a Scherzo and Trio. But it is no problem having the third movement be Presto and in compound ternary form.
So I was wondering, what do you think? Should I have the third movement be Presto? Or should I not go past Allegro in speed? I mean it would certainly be easier for me to play it if the fastest speed was Allegro but should I have a Presto movement in this sonata and if so, should it be the third movement that I have thought of possibly having at Presto or should it be the Rondo despite my doubts on having an A major piece be at Presto?