by the time you add all the tipping bits and the tray you'll be eating into your 2t payload of the tray.
The electric pumps are usually a lower flow pump turned at a higher RPM with the same pressure rating and perform pretty well, although they may be a little slower at higher loads, However in my experience with smaller cranes the lower performance can help with precise operations. Most cheap bolt on tipper trays are electric and I've seen them in up to 5t Tray (about 4.5T payload) configurations. I can also confirm that the hyd power available from an electric unit is greater than what the powersteering pump can deliver however the duty cycle isnt there.
If it was me before I started looking at my powersteering system knowing that my armstrong unit still works fine.. Id strongly recommend the compromise that will most likely suit you best would be to put a Demand diversion valve on the powersteering system, up the size of the reservior and then use the diversion side to run the powersteering with the primary side running the tipper/crane.
The draw back is, while youre tipping or craning the powersteering will drop off, but as you're not winching I dont think that will be a big issue and yes, If I was going to that much effort I'd also be putting a hydraulic rear mounted winch under the tray.

