I believe you have a choice ..
I mean, all I really sense, personally, for me is that .. .. I've known many people that have died, who seem like they would have so much that would make them be reincarnated to finish/complete/evolve from and to me that would relate with the concept/thought of having no choice .... because you would have to personally Finish, at some point...
But, something very strong in me, tells me that those loved ones of mine, who seem like they would have so much that would make them be reincarnated, actually wouldn't be/wouldn't have to because they learned so much inside, even if it seemed like they were completely at loss of the questions they had of so much.
Hopefully I'm making sense here.
Reincarnation .. I believe .. you Do have a choice. I mean put it this way, do you think .. your soul is just thrown around the galaxy and back into this Earth which we all can say at some point or all in all is our own personal hell (where we create our own heaven, to expand that into Changing the world)

??
Hopefully I'm making some sense..


Maybe you do have a choice and may you don't have a choice, but either way whichever it is, it most likely has a very very good reason behind it.