Anonymous wrote:I think you should save your money and effort and have the yard professionally tilled.
That will just till the weed roots into more parts of the soil. The vines need to be either pulled or killed.
I would combine the selective herbicide with your lasagna/cardboard plan. The cardboard works well for normal grass and weeds. It needs to be on for a good long time, like now till April. The really tough weeds will survive and you'll need to keep pulling them in the coming years. But selective herbicide plus lasagna will get you to a point where normal, hand pulling methods of weeding will be possible.
Mowing is also reasonable, if you don't mind having your yard a "lawn." Mow the ivy, bindweed, vinca, crabgrass, etc. and it will over time turn into something that looks lawn-like.