I think it would be good to go in there with a short set of loppers occasionally to knock down the ones that have been chewed clean. That way the goats can more easily access new material without getting cut up.
If I were trying to feed that material I would run my cordless hedge cutter over at every foot of height and cut a few feet into the face of it every week. Let them clean up what falls.
The goats shouldn't have any problem navigating the brambles, thorns and all. When I lived in New Jersey, I had some Alpines for awhile. Over time they ate 7 acres of wild rosebushes that had long tangled branches. Of course that wasn't the only thing growing on that land, but they willingly ate the rose and eventually got it under control to the point where I could pull out the individual plants.
Here in Hawaii I had an area about 1/8 of an acre that was solid thimbleberry growing under guava and persimmon trees, with some mixed grasses. The thimbleberry is incredibly thorny and difficult to tear out. I put 5 goats on that and they cleared it out in about 9 months, though they were moved to rotational pastures from time to time so that they'd get enough fresh browse to eat. They did a great job of getting that thimbleberry down so that I could get in there to remove surface rocks, downed branches, and trim the trees. Some of the thimbleberry is still growing back, but that's ok. It's now part of the rotational pasture system.
It's never too late to start! I retired to homestead on the slopes of Mauna Loa, an active volcano. I relate snippets of my endeavor on my blog : www.kaufarmer.blogspot.com
I've noticed that anywhere that's been growing Himalaya berries for some time has excellent soil. This may be because they start off in good soil, but I think they also improve it. Not something you'd plan on doing in one year, but a perfectly viable method where you do it over the course of five or ten years. With a hedge cutter it's a very quick chop and drop process.
Giant piles of rock and dirt placed around heavy equipment yards or just pushed up along the perimeter of an area that's being prepared for some use that requires a flat spot, become engulfed in these berries and soil results.
I think you re using the wrong type of livestock; sheep are easier to keep fenced in, and I can attest from personal experience that they will graze brambles out of existence in very short order. They will not grow back because they eat so close to the ground compared to other animals.
I don't have any blackberries on my land (I actually wish I did!) but my goats when clearing other overgrown areas seem to do a really good job around the edges, and also will sometimes eat/squash their way around making trails. If your goats seem to be slowing down with the clearing, you can try to make more 'edge' for them by slashing some trails, and also by stomping/slashing the stuff they've already been eating. You can also try throwing some alfalfa hay, apples or other treats into any bit they may have missed.
For blackberries I would avoid using any does with big or droopy udders, and I'd avoid using fibre goats. Meat goats, and dry or male dairy goats will do a really good job of it though.
One thing you'll need to think of is the fencing. You'll probably be fine as it sounds like there's a lot in there for them to eat, but maybe make the fences a bit higher than you usually would for sheep, just to make sure you don't get any escaped goats. Four feet high is usually a good height.
Related topic. I'm a bit south of the OP, but same general environment. I have a little under 5 acres total, maybe 2 that is heavily loaded with blackberries and other brush. Maybe 1.5-2 acres is grass. The balance is forested. I do have about 26 hens that right now get to basically freely range.
Someone mentioned sheep as an alternative to goats. Will they really eat out long established (10+ year) blackberries? Would a hair sheep like a Katahdin be a good choice? Will they be as fast at clearing that brush as a comparable number of goats like Boer or Kiko?
Goats, or sheep, for the circumstances I mention, if I wanted the land effectively cleared within 8-9 months how many would I need? Assume they'd all be weaned but still lambs/kids at acquisition. Basically I want to get enough in the early spring to do that job and be able to slaughter or sell them in the late fall so I don't have to feed them over winter.