We have the same problem, the garden was wild when we took over the house from the old lady who lived here. We actually used a strimmer to start with. After nearly 8 years I have it under control, but the only thing that worked for us was to weed,weed, weed. Keep absolutely on top of it and remove as much of the root as possible. If you can catch it while it's still a stump it'll come back as the medusa heads type growth, if you leave it till it's bushy then it'll seed. The membrane will certainly help under the gravel, but not sure how that would work in the beds - mine appears right up against the roses for example so no way to cover all that ground. We were told the only way to completely remove it was to excavate down 2 metres . That was never an option! Sorry not to be more helpful. (At least it's not Japanese Knotweed )
My garden is infested with mare's tail. It is everywhere and I can't keep on top of getting rid of it. I tried several applications of weedkiller over the summer - all over the area, but nothing got to it. I've heard that I should paint herbicide directly onto the shoots, but there is so much of it that it would take me weeks. I've done so much work on the garden this year and it would be lovely except for this nightmare weed taking over everything. Most of my garden is laid to gravel and it comes up and covers the gravel like a big nightmare lawn. I've had enough!
I am considering digging up the gravel and putting a membrane underneath to stop it getting through, but it's in all of my flower beds too - and in any available crack and crevice around the garden.
I feel like giving up. Please tell me I can kill this horrible stuff!