Hi,
Just to encourage you, I have a 10 pole plot that is completely and totally infested with bramble and bindweed. it's slow work but the parts of it that I have dug, have seen hardly ANY regrowth of either nasty.- and what has come back has been from tiny bits of root that i missed and very easily pulled out once they'd sprouted.
If you're keeping on top of the weeds anyway, you'll catch them before they start winding themselves around everything.
People keep saying that bind weed roots go down very deep. That is NOT my experience of bindweed at all! I don't know what kind of bindweed other people have, but all of the bindweed roots i am finding (and I feel i'm on intimate terms with bindweed these days! lol) they are in the top 8 inches of soil or so.... and I am digging considerably deeper to get the bramble out, so I would see them if they were lurking any deeper... so my advice is, to carry on what you're doing.
The teeny tiny white roots- they don't seem to regrow from my experience.
You can also grow through a membrane if you get impatient and want to get something in the ground where you haven't dug yet. Things like squash and pumpkin perhaps. Or trailiing cucumbers, even tomatoes?
I'm doing that this year, on a patch i am 'digging quickly' - (ie getting out the bulk of the roots but not doing through it with a fine tooth comb) Blocking out the light will help weaken it for when you dig it over properly.
I'm not a weedkiller advocate, though i understand why it would probably be the best option for some people who otherwise can't cope with the weeds and need to clear it initially- but its worth remembering that it's known to get into the ground water and play havoc with aquatic organisms, and also that certain weedkiller manufacturers can no longer state on their label that it is biodegradable and environment friendly, breaking down in the soil. They were dragged into court over false advertising, at least twice that i know of, and forced to take it off the label.... however the myth that it breaks down safely is still widely believed.