Please remember: the OP posted her question in the Organic Gardening Forum, where herbicides other than vinegar and similar kitchen-safe substances are not kosher. Certainly not glyphosate, etc. Conventional techniques are often recommended in other areas of THG, but this specific Organic Gardening Forum is just that: organic.
Re. the original problem, I had in mind a combination of what others have suggested:
--are two fences really needed? If you *own* this property, your fence can be removed.
--which would make the plants more available to...oh...
brush-eating goats, who will happily eat everything down to the ground: blackberries, ferns, weeds, etc. Many brush-clearing services these days operate using, essentially, "rental goats." They come with a human watcher/tender and the appropriate number of goats for X days, based on their professional estimate of your needs, and the brush/greenery/invasiove plants are history. Zap.
--or, if goats aren't available in your area, horticultural vinegar rather than kitchen-strength is recommended. Regular kitchen vinegar is 3% acetic acid; horticultural vinegar is at least 5% acetic acid, and I've seen mention of stronger stuff--although I haven't had any containers of it in my own hands. You (generic "you") can spray the stuff on the leaves of undesireable plants, killing them that way, or you can direct a small stream of vinegar toward the main root(s) of the undesireable plants. Once they start to weaken visibly, use a weeder (aka asparagus knife, dandelion knife, forked weeder) and get the roots out. It will take a few passes, but it will work. (I've used it against
Yellow Star Thistle, scourge of California.)
--a few hardy, non-risk-averse souls have used a propane weed torch. That may not be a very safe choice near a wooden fence! But, to be complete, I thought I'd mention it. Most plants (I.e., those
not evolved for a fire-dependent ecosystem) don't appreciate being burned off at the ground surface. I haven't used this method myself, but there are members of THG who have. Maybe they'll add their experience to this thread?
--although I conquered invasive Bermuda grass back in Berkeley by digging it out and sifting the roots out of the soil, I don't recommend that technique this time because of the ferns and their spores. As you've observed, the spores will scatter at the slightest touch. I'd recommend a combination of perhaps the goats followed by the vinegar *before* resorting to digging; that way, the ferns will be weakened ahead of time.
Hope these techniques work for you!
Cynthia H.
Sunset Zone 17, USDA Zone 9
What a great idea!