Sheet mulching over hard to remove perennials like Greenbrier

I'm setting up about a 1/4 acre of my land for a large annual garden and have cleared a bunch of bush using a brush cutter which drops this Greebrier thorn problem I'm having down to about 4"'s. From what I've read this can have rhizomes under the soil and can be hard to get rid of organically.

I'm planning on sheet mulching this area in 4 blocks - one with a hoophouse on it for winter growing.

Has anyone successfully sheet mulched over Greenbrier? I'm worried it may come up in a few years in my no-till beds and become a nuisance. I don't want o disturb this soil via bobcat or excavator b/c it has such a nice hummus and composted forest floor.

My plan is to hit the first layer with free horse manure/leaves -> cardboard -> composted cow manure/topsoil mix then be adding compost year to year - about 1-2".

I successfully sheet mulched lawn this way over the summer but this is a much larger area.

Any tips on reducing the likelyhood of the Greenbrier making it way through? Should I try cutting it lower to the ground?

Thanks in advance. Photo of greenbriar attached.

The rhizomes are close to the surface and do not break easily. If I were you I'd pull them out. In the long run, less work.

You can eat them: http://www.foragingtexas.com/2008/08/greenbriar.html

The young growing tips are quite delicious! They have almost a yeasty flavor, an excellent addition to a salad. The thorns are very sharp though and the growth pattern very invasive. We.enjoy the grwing tips foraged from nearby woods very much, but discourage the briars in our gardens and orchard.

These grow very well in woods in deep leaf litter, so mulching may not be an effective control.

Thanks - not sure if pulling a 1/4 acre of these is feasible but I could try. They don't slice with a garden spade either, they are pretty tough.

I'll have plenty of veg growing in this area so I'm not interested in growing these for shoots - no variety in diet there.

Matu- this is actually overgrown woods here in the photo-I don't mind it growing out in the wood lot but not in my annual garden.

I'd be interested in seeing if anyone else got rid of annoying perennials like this with sheet mulch.

FYI found an interesting article from 2014

http://permaculturenews.org/2014/09/30/sheet-mulching-aggressive-perennials/