Years ago I helped a friend out culling mainly fallow on a small piece of private woodland up on the South Downs that had no vehicle access permitted.
We modified an old fashioned folding golfing trolley to get the carcasses out to the truck. It was ideal as it had large wide wheels so didn’t sink too badly in soft ground & in itself was fairly light meaning we were not pulling that much additional weight.
Pulled the animal headfirst towards the handle, the back then cradled into the bits which would’ve originally stopped the golf bag falling sideways. The bottom bit was modified so there was a ‘shelf’ to sit the arse of the animal on so it didn’t slide down as it was wheeled out & we used to tie round the chest under the armpits & up to the handle from memory. Unfortunately all before the advent of camera phones so I don’t have any pictures.
This type of thing but more substantially made.
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One thing you need to be aware of with fallow is once they’re dead they become big heavy floppy lumps that aren’t easy to get up into the back of a vehicle. A ramp of some kind that you can slide them up will assist you immensely, as too will some sort of rope & pulley system - even if it’s just a rope you hook up between the outside seat hinges with a central loop that you can attach a simple doubler block to.
Back in the day when my carcasses all went inside my everyday vehicle I used an old ‘office moves’ / ‘teacrate’ box to contain all the mess.