Posted: 25/05/2014 at 08:17
Dogbowl - (I feel bad calling you that!!! by the way) : I had the same scenario a few years ago when I completely dug over a totally neglected garden. Everything had to come up, even the small lawn.
I had the same issue with lengths of root from half an inch to an inch thick under everything. Spaghetti junction! Nearly killed myself chopping them with a spade, cutting with secateurs and loppers. They were about 12ft long in places. I was told it was bindweed but there was no bindweed to be seen anywhere. But, looking at photos on the net, it certainly looked like bindweed. The only other conclusion I came to was that it was the end of the (!) root system of an enormous gum tree in the garden next door.
I'm afraid I had to do it all by hand. Took 4 days.
Yours may be something completely different but I sympathise. It was hell!