Hello Big D
I am sure your problem is shared by many and I appreciate your point about an intial dig. Woody plants are best removed with a sharp spade as they grow through most mulches. Only the main root 4-6in below the stem of bramble, sycamore and elderflower, for example, need removing as the remaining roots will then rot. Nettle and ivy can be mulched, for a year to be sure of them dying. So it is not a total dig everywhere.
On the other hand, the plastic debris you describe is better removed, I am not sure how worms and other soil life may be harmed by it, so it appears that ye, an initial dig is worthwhile. At least it is once only and then you will have clean soil. The first year or two are always the most demanding, so well done and good luck.