As much as I hate to advise the use of chems, that might be your best bet, I've not had much trouble pulling up vinca minor, but it takes a few years to get it all.
Plants with slick, glossy, waxy leaves are impervious to most spray that's available to home gardeners, if you have a sprayers license, then there are some that can kill them.
The one I have trouble with is wintercreeper, creeping winter berry.
Just try to pull it out! Ha!
The best spray I've found is called crossbow, it nukes everything!
Overspray will systemically kill or damage plants around it, and drips in the soil will be taken up by surrounding plants and kill them too!
Best of luck!
