I did the first year's event on a hard tail based on Ash's original suggestion - after all he scouted and rode all the trails on his hardtail, although he's a far better rider than I will ever be.
My only comment on the hardtail approach is that over the course of the week the pounding takes its toll, and if I was to do it again (and I really would love to) I'd go for the full sus option so the muscles were marginally less tired in the latter stages.
As Rob has also pointed out, if you're happy with your bike then just use that.
Stages are mostly downhill, but occasionally they do have climbs in them. The linking stages are not timed and they are where the majority of the 'updulation' is found.
One thing to be aware of, the on-paper stats for a typical days riding on the TP do not do it justice. They may be short days (distance) and with manageable climbing numbers (particularly as the uplift takes out some of the sting) but do not underestimate it. It is a tough week, but oh so rewarding for the riding, scenery, organisation and camaraderie.