I was also surprised Pappajunk didn't start with a junk mower deck. What he has built so far is pretty impressive fabrication. Since he is using a mower spindle with a belt drive pulley, maybe he can substitute a gas engine if the hydraulics aren't powerful enough?
If the sticker bushes are multiflora rose, a lot depends on how thick the stems have become. Using an attachment capable power trimmer head would allow you to easily change between a steel circular brush cutter, a hedge trimmer and a pole chainsaw style cutter.
A potential issue with a regular mower deck is hitting a large enough stem could shear the shear key in the mower engine. Having a belt drive system like used in one of the walk behind trimmers might help take up the shock and avoid this to some degree.
As for what kind of gas engine that can handle operation on a slope, the 2 hp Honda GX50 is a small four stroke that is 360 degree inclinable.
Honda Engines | GX50 Mini 4-Stroke Engine | Features, Specs, and Model Info