That "custom manufactured exclusively for us" is what tipped me off. I know I won't pay Deplorable's price. It's not even a nice pump. I'd buy it in an off count spline and machine it to what I need before I paid that price. It's less likely to be something odd and specific for their use and more likely to be so they can gouge you on the back end when you need parts. It's immoral. It's also a concern that people should have when buying a tractor like this. What happens when LS stops supplying this part? The tractor becomes a paperweight. When that happens, the LS name will be in the gutter. I smell greed.
I'll find out and report back.
It's possible that the pumps off the MT4 series tractors would work. They are a 9.9 gpm pump, which would probably help quite a bit. The suction side might be a different size though.