To a degree nut grass spreads like quake grass by rhizomes.
The white ones are easy to control but they also get the dark ones that spread horizontally like main rhizome of quake grass.
I had a hillside of nut grass once and dug out a 12 by 12 area, raked it and prepped it for sod.
Two years later the nut grass popped through the sod.
I do not know how large or compact your vines are but in an area dig a hole 12 deep carefully to observe the nut grass rooting system
Paint it with nut grass killer and see how much dies; that way you will know how far that system goes.
I killed mine with nut sedge killer, which up here is oddly not available so I had to mail order it.
When I sprayed where it was in the flower garden I held the sprayer just above the ground, inches and did put no more down than to wet the sedge.
May the phates be with you.
Worst case scenario, dig out your vines the way you do for repotting and then blast the area with sedge killer.