This time of the year (assuming you’re in the northern hemisphere, apologies antipodes) you can probably toast the annual weeds by laying landscape fabric over them, just check it often and don’t leave it on long enough for the perennials to grow through it. Pulling weeds at that scale sounds pretty tough! Plastic might be more effective, if you can find a roll that is the right proportion for the rows. Of course, it’s easier said than done, but we’ve had success controlling quack grass with woven fabric – only during the summer heat.

Do you have access to any good mulch to try around the vines (after suppressing weeds)? I would be worried about the learning curve working with perennial ground covers – you might end up with different plants but the same problem. Maybe a ground cover trial area is a better way to start.

I don’t know anything about vines – could you use very shallow tillage passes to start suppressing the weeds?