new 1st year grower - how would you support these bines?

I'm growing next to a fence that's about 10' 6" with southern exposure. I just planted 4 rhizomes, 3 feet apart in a line along the base of the fence, a couple feet away from it. (Actually the bottom half of the fence is a rock wall, though it shouldn't matter.)

I'm not gonna grow the bines directly up the fence -- it's not gonna end up being tall enough, plus it technically belongs to the city and it's got flowering vines growing on the other side of it that can come through the cracks between the slats. (It is a solid fence, there are no big spaces you can see through or anything, but of course there are spaces of a millimeter or two between the slats.)

Even though the fence belongs to the city, I don't mind putting nails or eyelets or whatever to support some rope or twine. But I couldn't build big structures or anything attached to it. (Not like I'd expect to for this anyway.)

I don't want to set up anything higher than the fence -- my mother rents this land, and the owners of the park can get strict about their rules -- for example, giving her a hassle about whether her shed is actually two sheds connected together, and you're only supposed to have one shed. I don't know about specific rules that might apply to my situation, but something going up close to the side of the fence, the same height, isn't gonna draw much attention.

So anyway, four lengths of twine going from each crown to the top of the fence would only be maybe 11 feet of growth, so I need to think of a system where I can slacken the twine where it gets close to the top (read about this on some other threads), or incorporate a lot of zigzags, or something. But one problem with the slacking method is that the bines might start grabbing the fence. I might need a setup that incorporates poles that go straight up, or almost straight up, from the crowns, so the bines aren't too close to the fence when I slacken them.

Anyone done something like this in a similar situation, or have any ideas?

Thanks!

The issue with the slacking is that your going to end up with a giant knot of leaves and bine at the bottom on the ground, probably rotting due to contact with the ground.

Your best bet is to make a really long run and once they reach the top train them horizontally as best you can.. You'll have to keep on top of them every few days though or else they may stagnate trying to grow up off your horizontal and just turn into a big bush falling over itself due to the weight.

Ideally poles 20 ft or so could be placed on your side of the fence, but I understand not rocking the boat.

I did the "paying out line" theory, but the "paying out" was from 15 ft or so, and the stuff overgrew my played out line in no time flat.

Paying out line does not mean that you have to have line laying on the ground, but you would have to tie bundles of it and hang them from grommets on the fence or something.

The bines need more spacing that way too.

In full growth you will never stay on top of it. I swear the stuff grows 3 feet a day.