It will take a lot of commitment, patience and perseverance, but I’m sure it’s possible. I wish I could offer buckthorn-specific advice, but that’s one I (thankfully) haven’t had to deal with.
If you run into multiflora rose let me know. I’ve single-handedly removed 15 acres of multiflora without the use of herbicides, digging it out with a specially modified shovel that cuts through the roots just below the crown. It was a lot of work, but not impossible by any means. Actually went faster than I expected. So many people told me it was impossible to get rid of without herbicides, and they were wrong, so don’t let anyone discourage you! Buckthorn probably isn’t impossible either!
As for the Vinca, it will die if you pull it and leave it scattered loosely on the surface to dry out (whatever you do don’t pile it!) but hand pulling is quite labor intensive because you are working on the ground. Mulching for a year with something solid works, that can then be dragged to the next site. I’ve used heavy duty black landscape fabric but I dislike the way it gets holes and vines grow through it. I far prefer sheets of used steel roofing for mulching Vinca, because they are much more durable, and easier to move each year. The Vinca patch I’m chipping away at by a combination of methods only started out as about two acres, so not quite the scale you’re talking about. And I’m not sure how the parks would feel about old steel roofing out there.
I would suggest largely ignoring the garlic mustard until perennial invasives have been dealt with. It’s really not the worst when it comes to crowding out native plants, and you need to prioritize.
I would also strongly suggest focusing on a smaller area to start with, even if you have to basically choose one at random. Least infested would be ideal, but you can also just choose an area you personally like, or everything within 100 ft of one side of the trail, or something else, and give it clear boundaries. Sometimes people bite of more than they can chew and end up making things worse. Yes, pulling will lead to more seed germination. You pull the same area again every year and only expand the “defended zone” a little at a time, as the first area you did gets easier and easier to maintain. The bit by bit approach also minimizes disturbance to wildlife. Birds that nested in the buckthorn in the first area you clear, can nest next door to it, and native shrubs will be establishing in the first area as you slowly expand each year.
I would try to clear maybe half an acre of buckthorn to start with, and give it at least a year to see how your method is working and whether any adjustments in strategy are needed. Start mulching or pulling Vinca in the same area, to make way for native plants. Once you know what’s working, expand this little bastion of high quality habitat outward as time and energy allow.
You didn’t mention, are you taking this on single-handedly, or with a crew?
