If you have that much compost, you would have been many backaches ahead to just cover what you started with with compost and let it sit for 3 months. If you really want to plant a cover crop, vetch is fine. I like clover, too.

Rye, Field, Winter, or Cereal, is a winter crop, as is vetch. These are planted in the fall and grow through the winter. For spring planting Oats would be a better choice because they germinate in cooler soils and grow quite fast.

Don't forget about buckwheat. Ohhhhh taayyyy! It grows super fast, germinates at low temps, smothers weeds, and looks great. It's even easy to till under. Remember though that it is rather tender and will be killed by hard frost. Don't let it go to seed or it can become a weed.

Buckwheat is a summer green manure / cover crop and needs fairly warm soil temperatures as well as air temperatures to germinate and grow.

I plant rye grain and hairy vetch as a fall cover and it germinates well in late September or early October. The rye has a dense and fibrous root system. I seriously doubt that vetch will germinate later this month unless we have some unseasonably warm temperatures. If you do chance planting the vetch remember to coat the seeds with an appropriate innoculant before sowing. A single cover crop is beneficial but don't expect miracles. Soil building is a slow process and requires perseverance.

Buckwheat will germinate at temps as low as 7 degrees C.

Here is a link that might be useful: About Buckwheat

Buckwheat may well germinate in soils as cool as 45 degrees F, I've not had that happen for me, but since it is a warm weather crop it will not grow as fast in those cooler soils. Oats will. In cool soil temperatures you could grow Oats as a green manure crop and cut them down in about 30 days while it may be 10 weeks for the Buckwheat to get there.