Save your time and money on the phone call, NeilBaker.
It is not within the DVLA's gift to offer (or refuse) the DD Rehab course. It can only be offered by a court at the time of sentencing. The court decides whether the course would be appropriate and also sets the cost.
There is also some confusion creeping in here. The reduction in disqualification you are seeking is nothing to do with the completion of the DD Rehab course. All drivers (regardless of the offence(s) committed) who have been awarded a ban of 36 months or more may apply to the court to have the ban reduced after (I think, without looking it up) two-thirds of the ban has elapsed.
The court will look at each case individually and consider (among other things) the effect the ban has on the driver, the driver's conduct since the ban, and (most importantly in your case) the reason the ban was imposed in the first place. That is why I say that the three year ban, being the minimum mandatory that was allowed in your case, is most unlikely to be reduced.