I don’t know where you are located (Nevada?) but many draft stallions are not advertised, nor are their owners set up to collect and ship semen. So your best bet is to start making contacts within a reasonably local distance. Since a lot of the “sport” draft crosses here in the US come from Canada, I think it can be hard to pin down US draft stallions that consistently produce sport type offspring. I think that considering a RID is a good idea in that the stallion would be more of a known quantity as far as aptitude as a riding horse.
Along that vein, I disagree with limiting yourself to Percherons. Yes, there are a number of really nice Percheron cross hunt horses out there, but there are also a lot of nice Clydesdale crosses out there as well. Breeding draft crosses is like breeding any other type of horse–you really need to take into account the individual parents and there still can be variability in offspring.