If it were me, I would bite the bullet and use Roundup on it, and be done with it. Otherwise, there are no magic bullets...

I really really don't want to use a chemical solution. The garden had been full of so much noxious trash and chemical jugs when I got it, that I just can't bring myself to add to the toxicity of the earth.

I suppose I'll just keep digging.

I had Vinca years back and sheared off the top and pulled it out from the roots. I have a feeling your plant has grown like my Plumbego that was once a bush and now everywhere. I love it's blooms but the suckers are everywhere . Had to put up shadecloth but those suckers broke right through. In my case these Plumbego's look so nice in my front garden and take alot of trimming. I wish you well.

If you dig it out, you'll get most of it. Some will resprout. You must dig it up again. That's the only way. To keep after it. You will win eventually.
Vinca has its uses, primarily as ground cover over large areas under trees. Small gardens or cultivated spaces, it's no good.

Thanks!

I figured I wasn't the only person who had dealt with this.

Rent some goats, maybe, for a one-time "all you can eat vinca buffet"? They can also take care of other weeds while they're around. I see them here in the East Bay all the time, chewing down brush. :-)

I have a similar problem up here in Richmond with oxalis. I decided to use a smothering mulch. I put down thick layers of newspaper, sprayed it with water, and then mulched over it. NOTHING is coming through it, 9 mos. later. My neighbor is a landscaper, and she did the same thing with cardboard (but I think the newspaper goes down smoother). I just laid the paper around existing plants and poked holes in the newpaper for my new plants. If it comes back, I'll just throw some more newspaper and mulch on top. Easy.

I did use Roundup around our arbor, where the newspapers left small gaps around the feet and there was no danger of killing my other plants. I read somewhere that Roundup doesn't stay detectible in the soil, so it's the least harmful chemical to use.

Roundup breaks down quickly, but the newspaper or cardboard mulch is a good idea. For the stuff behind the lattice, though, Roundup is going to be the best way to go.