I am assuming your cutter is a 540 PTO cutter.
The issue is that if you buy an off the shelf replacement gearbox with 20 spline shafts... this 20 spline box will be geared for 1000 PTO. The gearing within the box will be different from the cutter's original gearing and that's going to change your blade tip speed.
If you can somehow confirm that the gearing is the same as your existing gearbox then it will work. I don't think that is going to be the case. This is why I said you need to replace the broken shaft and not the entire box itself. $611 is high as crap. Ouch.
I am surprised you can't get a NEW 540 diverter gearbox and then you'd be ok. They obviously made those cutters in 540 that's what you have. Call that German Bliss place if you want I deal with them and they will actually help you. They know more about Bush Hog parts than Bush Hog itself knows about their own equipment not kidding. You just need the serial number off the cutter.