I'm putting in my first hops this year, so I can't speak from experience but this is what I've got.
From the info that I've gathered it doesn't sound like you want to cut the bines early since a lot of nutrients flow back into the rhizome system before it goes dormant for the winter. Of course they were talking about harvesting, but I would think that cutting off bines in the middle of it's growth cycles could be rather detrimental. Since it's already in a pot for easy transport, my first thought would be to pinch the bines off as they emerge & just don't let it send up bines until after the move (if it still will, lack of experience so I don't really know how it would behave at that point), which would still give you a little bit of growth & let the plant get back into it's annual cycle by next year.
The other thought would be to do put a wooden dowel 4-6' long in the pot, tie your string off as normal at the bottom, hook the first 4-6' of twine to the top of the dowel, leaving all the extra twine you need coiled up. As the bines climb the string, you simply loosen the knot & feed it more string, eventually causing the bines to coil up. I've heard of others using this method for apartment balcony/small space grows. The biggest thing is to make sure the coil is able to dry out after it rains & such, but from those I've heard doing it, it sounded pretty simple.
Best of luck however you go about it!
Lee
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BN Army // 13th Mountain Division