The simplest way to deal with your situation is to prepare an area now to be replanted later this Fall once the vines die back. I normally prepare an area during the season and then lift and transplant in the Fall after everything has died back. The biggest thing that folks don't take into consideration is that by doing this in the Fall, the soil is still relatively warm (compared to Spring) and this will give the new roots a chance to begin to get settled in and give you a great start next year as they'll grow until the soil freezes. If you don't have the space to bury them somewhere until you get the area cleaned up, find someone who does. The biggest thing is to keep them in the ground as opposed to pots. That's just my opinion but the earth will take care of them appropriately during the transformation. If you can't find a temporary location, I guess pots would be the next best thing - but make sure you have a big enough volume of soil to help moderate any big temperature swings that may occur during the switch.
Mulch in the hopyard is a good hedge against weeds but if you have established perennial weeds, you have to take care of them first or you'll be fighting an uphill battle for ever. Make sure the area is clean to begin with and then utilize the mulch or compost to help lessen the weed problem, AND THEN STAY AFTER IT. Weeds are a pain in the ass and very very sneaky. Turn your back or go away for a few days and bad things can happen. At that point you'll be playing catch-up and unless you're really good, the weeds will win. And don't worry about harming your crown. Sure, you'll set it back a little, but if it's had a chance to grow and develop this year there's plenty (an excess) of food stored up for you to have great success next season.
Whatever you decide to do, make sure you have plenty of beer on hand to help make the whole process more enjoyable. Over and out!