How to kill cover crop
Okay, I'm new to this so please be kind.
I have dense heavy clay with little to no organic content and want to plant trees, shrubs, perennials. So for the past 1.5 years I've been adding things like compost, manure, coffee grounds. Last year I brought in 6 inches of compost and manure, planted a cover crop (rye, vetch, legumes, diakons) then when crop was 4 feet tall I chopped it down and tilled everything under. I then planted a second cover crop in September, let it go dormant, mowed it in Feburary and laid down another 6 inches of compost on top - did not till this time. I then laid black plastic on top with hope of killing the cover crop prior to planting trees, shrubs, perennials.
The plastic has been in place now for about 5-6 weeks but it has been cloudy and damp, likely not warm enough to toast those seeds. So, any suggestions as to how to suppress the cover crop from coming up through future plantings?
Someone had suggested using Round-up, wait a week then till everything under, wait two more weeks then plant trees etc., and finally add Surflan. Other suggestions?