I'd start by cleaning/replacing the suction filter in the hyd oil sump. Once you are sure you are getting clean oil, install the new pump. Before starting the tractor again, would go to the FEL joystick control and remove the large cap that covers the relief valve. ( most are on the bottom of the valve ) I'd open the relief valve until it will hold almost no pressure. You will know you are wide open when the FEL won't operate anymore. Then slowly adjust tighter and tighter until the FEL will just lift the front end of the tractor off the ground. That said, this is a open center hyd system and should bypass to the relief valve in the 3 point when ever the FEL is not used. If the pumps crap out only when using the FEL, I'd work on the relief valve, could be crud from a dirty filter loged into the valve seat. Sure costly to be wrong, $400 a pop + labor. I'm suprised that the key didn't shear in the drive coupling first.
Chris