Seems like you could squeeze a lot of batteries in the area if you removed the gas engine, exhaust, muffler and gas tank. Not sure how the 180 is laid out. One electric motor to run the variable volume pump and another to run the lift/steering pump. You don't need a PTO for anything, do you? If so, I'd go for a third electric motor.
Have you thought about buying a carcass of a 180 and putting one electric motor at each corner? I wonder how you could get them to function without some sophisticated controllers though. You know how if you are standing still and rotate the steering wheel to the left and the front and back tires on the left roll toward each other while the tires on the right roll away from each other? How would you accomplish that motion with just electric motors at the wheels? How would you coordinate it if the unit was in motion? And most importantly, would you have brakes on electric motors if they had to free wheel, too. Seems you'd have to add brakes as well. I don't think you economically could do all that, so that means sticking with the hydraulic pump turned by an electric motor.
Then there's the question of how many pounds of batteries would you have to use to replace the HP of the gas engine and get a reasonable run time. Will the carcass of the 180 be able to support that much weight and still have a usefull capacity at the FEL? Will that joint that holds the two halves together be able to take the stress? Will the wheel motors be able to carry the weight? And what about hydraulic cooling? With an electric unit will you have to have an electric motor turning at 3600 RPM(or gear a shaft down to turn the pump at 3600RPM) constantly to supply the hydraulics, then use the treadle to control speed and direction? Or can you rig up something that senses treadle motion to kick in the electric motor at 3600 RPM. That seems like it would be hard to get smooth operation.
Whew! That's a lot of stuff to consider. I'm sure there's lots of stuff I missed and lots of stuff I don't understand the workings of. However, it just doesn't seem practical, but you already mentioned that part about horse people, and I have met a few. /forums/images/graemlins/wink.gif
If it were me, I'd just get a propane conversion. They are readily available. There were two that I was looking at for our 8HP generator. One was just a carb replacement and the other was a dual fuel conversion kit. I'd go for the full carb replacement kit. That way, you just switch carbs and add a supply line for the propane. Mount the propane tank on top of the engine hood somewhere and convert the gas tank to a sprayer tank for weeds around the barns.