Green manure before summer planting

There's a summer flower bed in between my asparagus that's not had a lot of organic matter (apart from woodchips in the winter) and I'll be planting red dahlias, pink and maroon sunflowers and white cosmos in the summer.

Around the asparagus beds are 2 "grass" paths that used to be infested with couch grass but, after a few growing seasons of mulching and hand weeding, that are now practically weed-free but the soil is too dry for grass seeds. 

I thought these areas would be ideal candidates for a quick spring green manure treatment.

The main issue at the moment has been the dry weather. The green manure seeds need rain to get established and I have nematodes for slugs and red ants waiting in my fridge that will need watered into wet soil. 

That's not happening yet! Another glorious sunny morning. I can't enjoy dry spring weather as a gardener...