....The problem. Reverse is a mess. The boat will go where it wants, period. .....You can push the tiller any way you want, until you get a good speed up it does not matter...
While many boats do not handle well in reverse, many are in fact quite good. None of them, however, will steer well until you get good speed up. In order for the rudder to have any effect there must be flow past it.
The configuration of the Tartan is not one I'd expect to be particularly bad in reverse, (compared to a typical full keeler, for example) but I've not driven one.
A three blade prop may get you going a bit sooner, and allow attached flow more quickly, but you may also suffer more prop walk and of course more drag under sail.
It's important to not try to steer by tiller until you have speed, if you try to turn the boat then you are really just putting on the brakes and probably making things worse.
Find some open water, and practice backing up with the rudder amidships initially, see how she walks and at what point you have enough speed to think about steering effectively with the rudder.
All that said, however, there are boats that simply won't go along with any plans to go where they are pointed when backing... and that's tough if you have one of those.