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Should I stick with Scherzo form or turn it into a Sonata?

I have completed the A section of my Presto piece, or at least what I have thought of for it so far. It is quite quick at quarter note = 190 BPM. This is another piece for  which I was aiming for a humorous character and I think I have done it. I titled my piece Presto in D major, because I wasn't sure if it could be considered a scherzo or not, but I did know that 190 BPM is well within the range for Presto. I also am not sure if I should stick to your typical scherzo form or if I should expand this out to a sonata form and have what I am now considering the A section be the First Theme. This is your typical Scherzo form: 


 
I sometimes, especially in Beethoven and Chopin, see diversions away from this form and more towards sonata form in their scherzos(most commonly a coda is added, but sometimes the B section is extended to be more like the development section of a sonata). But currently, what I have would be the A section if I stuck to your typical Scherzo form. In comparison, here is your typical sonata form which I am thinking of possibly expanding this piece into due to the sheer speed of the notes. I  mean, most Scherzos that I hear are at least 5 minutes long. Anyway,  this is your typical sonata form: 


 
And here is what would most likely happen if I were to expand the piece from typical Scherzo form to Sonata form: 


 
It isn't the speed or how humorous it is that is making me question whether what I have right now could be considered the start of a scherzo. Rather, it is the time signature that is making me question it. Most scherzos are in 3/4. What I have so far of my piece is in 4/4 and the only simple time signatures that it could fit into are 2/4 and 4/4 because of the Alberti Bass in it. That isn't to say that you can't have Alberti Bass in 3/4, you can. But the Alberti Bass I have doesn't fit well into 3/4. Here is my piece so that you can give feedback on it: 

https://musescore.com/user/50070/scores/5745153

And should I stick to the Scherzo form and just have it be a 2 minute Scherzo? Or should I expand it into a longer Sonata Form that might be say 10 minutes long at the same Presto tempo? 

Notation be like

So I usually am not in the presence of staff paper, and I absolutely love graph paper for many things, so I created my own system of notation for when I have graph paper but no staff paper. It’s rudimentary and inefficient, but it makes practical sense. It’s not really meant to play off of, it’s more meant to keep track of rhythms and pitches for future use. Currently I’m using this system to transcribe and transport the sax solo from Youngblood Brass Band’s “Brooklyn” into Flat.io without changing tabs or removing instruments. I’m mildly proud of this system; I’ve used it in the past, up to a year ago, but I’ve refined it.