I am no expert on livestock, but I question whether the goats and pigs will eat the white oak and poison oak. If it's too woody to eat but not large enough to cut with a chain saw you may be better off with a tractor and mower.
I've been clearing/thinning a 10 acre woods and found that a flail mower does a great job of shredding the multiflower rose, young saplings and poison ivy. The larger material (3' - 6") is cut with a chain saw to five foot lengths and put in the bucket and larger logs are skidded out to the field for processing.
Since you desire a savannah at some point in the future, I would think a CUT would work well for you.