A mini track hoe would be faster than that small dozer in steep terrain. If you build a road suitable for vehicles then rent a large hoe. Pull/dig from the up slope and put it down hill in front of you. One track will be on the fresh cut the other on the spoil you just put down. keep the machine level at all times. A track hoe can get it surprisingly level and smooth that a tractor and a blade could finish.
If you have never been on a hoe then find an operator.
As far as erosion you will need to be considering that during construction and have the road/trail laid out, this will help seeing how many if any culverts you might need.
This really isn't rocket science. Just imagine what the water will do when looking at the constructed road. Water bars, sediment traps, culverts all could be used and some other techniques will keep the road stabilized for a long time.
If you have never been on a hoe then find an operator.
As far as erosion you will need to be considering that during construction and have the road/trail laid out, this will help seeing how many if any culverts you might need.
This really isn't rocket science. Just imagine what the water will do when looking at the constructed road. Water bars, sediment traps, culverts all could be used and some other techniques will keep the road stabilized for a long time.