Weeds in my vinca

this is our first spring in our new old home outside of Philadelphia. We have about 3 acres of mature and well kept gardens and landscaping. While we have been doing ok keeping it as beautiful as we found it, there is one area I'm struggling with. We have vinca in a very large circular bed. There are so many weeds (not sure of the type) coming through the vinca, I can't possibly keep up. I did not use the preemergent weed granuals in this area (maybe that was my mistake). I'm worried that the weeds will choke out the established vinca. What can I do? I'm hoping the only answer is not to pull all of them bc it will take me days! Please see photos.