Well if you have all the VCAP's/VCIX then yes you can submit whichever you want but if you are going submit for CMA then you still have to submit a vSphere design due to the obvious reliance of vRA on vSphere. Personally I would recommend DCV first although it does depend which you are doing much more and which you see the most benefit aiming for. For you project did you do the design for all of the components? As you have to be the architect of the designs to submit them for VCDX and from my expereince that is normally done by three different people.
As for the same date no I dont think they allow it as far as I am aware and if you are a VCDX already you dont have to defend or do the scenarios for subsequent submissions so I would recommend that route.
Here in Brazil is a little bit different. I am the only resource in the company who has the skill to design the Service Provider project.
And the project has 3 steps and does not deploy everything at the same time.