Yes, she is short backed. Call Rocking R Saddlery out of Idler Alabama. I know you could probably have one made from them. They use the Steele Equifit trees which are one of the best in the industry. I had a saddle from them a couple years back. That gaited saddle fit not only the TWH I had at the time, but also the very wide shouldered paint mare my husband has. Every saddle before had pinched that paint mare, but this one fit like a glove. Wish I still had it, but I sold it with the TWH.
They have some beautiful show saddles now and I am sure a reiner wouldn't be a problem for them.
Oh and I find their prices pretty reasonable too.
Good luck in your search!