Finish/Grooming Deck Made to be Run Backwards?

[955Lincoln]

Hi all, I have a bit of a dilemma. I would like to buy a 3-point finish mower deck for my Carraro TRX. This is the tractor where the seat and controls can spin 180 so there really isn't a front and back to this tractor. I would like to run it backwards with rear wheel steering similar to a Kubota F3990 or any other front deck type mower. Just a guess, but I wouldn't think that a standard deck would do too well with the discharge pointing forward and I'm curious if backwards running decks are available. Then I'm also not sure if I should get a rear or side discharge if backwards decks are available.

Thanks for any thoughts and input.