Hi Mary, Thank-you for your question. You have one of the most invasive plants that people purposely introduce to their gardens and it is very difficult to get rid of. I also believe in using organic methods but in this case it is going to be hard. The littlest piece of root left in the ground will sprout a new plant. You will need to dig up all the perennials you want to keep and put them into pots or another garden. Make sure that crown vetch roots are not included along with the plants you are keeping. Then you need to screen the soil pulling out all roots you find. Make sure these roots go off to the dump or burned. This is the only organic method I know of.
If this seems like too much work you could (I can't believe I'm writing this but I know you are desperate) use Weed B Gone or Round Up. You can either remove all the plants you want to save then spray the whole garden or put the herbicide in a container and either "paint" the leaves of the crown vetch or wipe it on with a cloth. You could also put on form fitting rubber gloves and put jersey gloves on top of them, dip your fingers into the solution and then wipe it on the leaves with your fingers.
No matter what method you pick you have a difficult job ahead of you. But it is well worth the effort because it will only get worse.
I wish you well brave warrior. Bye, Diane