Tempo disagreement in rhythm and notation, what to do?

Okay, so I am writing this "Adagio" piece for piano and cello after a bout of composer's block. At the beginning 8 bars, I have a very rhythmic theme in C major. This rhythm gives the feel that it is at an Allegro tempo. But the tempo that is notated is an Adagio tempo, thus the Adagio in the name of the piece. There are 3 options that I could do as far as the tempo is concerned. Here they are:

Option 1: Adjust the time signature to make it fit into an Allegro tempo

This is one of my options, changing the time signature to make it an Allegro tempo. There is just 1 problem with that. My piece is in 3/4. If it were in 4/4, I would change it to 8/8. If it were in 2/4, I would change it to 4/8. But changing to 6/8 is going to change the meter from triple to duple. If I change it to 9/8, I would have to calculate how much a dotted eighth and a sixteenth in the original 3/4 would correspond to in 9/8. And of course, this would mean changing the name from Adagio in C major to Allegro in C major

Option 2: Adjust the melody so that the syncopation is on the eighth note rather than the sixteenth note

This keeps the notated tempo and time signature the same. And it makes the piece sound like it is at an Adagio tempo. But then, my already long notes such as dotted half notes are probably going to be too long. So, I don't know how well this option would work.

Option 3: Leave the first theme alone and let the second theme give that Adagio feel to the piece

This conserves the entirety of the rhythmic first theme as it is. To contrast the rhythmic first theme, I would have a more lyrical second theme. This second theme would feel like it is at an Adagio, subverting the Allegro expectations of the first theme. 

Do you have any suggestions as to what I should do for my piece to resolve this tempo disagreement? Here is the first theme:

Does the fact that the title doesn't match the feel matter to the integrity of the piece?

31 minutes ago, aMusicComposer said:

Does the fact that the title doesn't match the feel matter to the integrity of the piece?

 

I guess not, since I have already gotten started on a more lyrical second theme(I have the cello melody of the second theme settled, and now I'm figuring out how to accompany it in the piano) for the piece. It's just that I have never had a tempo mismatch to this degree before, even with dotted rhythms and sixteenth note rich pieces, so I wasn't expecting my "Adagio" to feel like an Allegro. At most I was expecting maybe a slow Andante feel if there was going to be a tempo mismatch.

A tempo mismatch is something you create. It doesn't come out of the blue.

If you want something to sound as an Adagio you have to write the proper duration of notes and the proper speed. Changing the time signature doesn't change the speed at all.

If you have a second part that sounds Adagio with this approach you show, and on the other hand you are happy with how sound this first part you have several options. What you can't do is saying something is an Adagio when has the speed of other tempo.

19 minutes ago, Luis Hernández said:

A tempo mismatch is something you create. It doesn't come out of the blue.

If you want something to sound as an Adagio you have to write the proper duration of notes and the proper speed. Changing the time signature doesn't change the speed at all.

If you have a second part that sounds Adagio with this approach you show, and on the other hand you are happy with how sound this first part you have several options. What you can't do is saying something is an Adagio when has the speed of other tempo.

So, you're suggesting that I double the length of all the notes of the first theme and consequently the transition(I take a motive from the first theme and sequence it for my transition, adding some countermelody between entries of the motive in each instrument), even the already long double half notes? Thus turning this:

into this:

OK. It all depends what you want it to sound.

If you want the speed of the first example, call it Allegro, put quarter note = 140 and change the value of the notes to sound like that.

If you want it to sound as the second one, call it Adagio and leave it as you've written it.

That's what I would do.

man...this is great conversation.   I agree with @Luis Hernández. do what he says and you'll be good!