I don't know of any upper level stallion owners that would breed to any sort of stock breed. The owners of high quality stallions are selective of the mares they breed to.
When I was looking for a stallion for my mare many stallion owners asked me for her show records, her blood lines and the results of previous foals she has. I was also asked what the reason for the beeding was, the plans for the foal and if I would be considering breeding the foal in the future if the foal proved to be quality.
Its all well and good to go "I would love to breed my mare to this stallion! He is so amazing!" but at the end of the day, owners of higher quality stallions are selective. They don't want to beed their stallion to any old mare that crosses their path. They want to make sure there will be the best possible outcome of the foal.
If you are set on breeding your mare, aim for something that would actually cross well with your horse. Such as a TB or QH.
BB ~ 2014 Trakehner Bratty Mare ~ 1993 CSHA Em ~ 2007 Standardbred