I'm interested in this as well. The place where I'm living is coated in periwinkle, morning glories and english ivy (not to mention tons of little common buckthorn plants). There's a space in front of the house that has nothing but periwinkle growing and I'd much prefer to have some shade-tolerant plants & mushroom logs rather than the periwinkle monoculture.
I feel like a permie-minded approach might be the following, which I will also attempt this year:
Gauge interest for vinca minor starts with your local seed-saving society, freecycle group or kijiji/craigslist. Offer those starts for sale, or for free if people will come and remove them themselves. Transfer some to pots if you really want to keep some around in a more manageable form.With whatever is leftover, have a periwinkle pulling party. It may be a small party thanks to the pandemic, but I find tuning into my favourite radio station (WFMU) makes any garden task go much quicker.After disposing of all the periwinkle you pulled (everything I read says to just bag it and send to the landfill), lay down a bunch of cardboard, soil and/or a bunch of mulching materials to completely block out the light for any roots that were left below. You can keep adding mulch over time, and/or plant something on top that will continue to smother the area and make it extremely difficult for the periwinkle to pop up again, such as squash (if conditions are right), or some of Sepp's recommendations for heavy-feeding fast-growing plants like turnip and sunflower. But ultimately, I'm sure you could play with those plants and plant anything that you'd prefer instead, especially if you're putting a good chunk of soil over the layers of cardboard.
In my research I found this neat freebie for dealing with invasives.
http://conservancy.bc.ca/wp-content/uploads/2017/10/InvasivesFreebie.pdf
Good luck!