my guess would be that the rhizome would survive either way, i mean hops are practically a weed, it's a hearty plant. Examine the worst case scenario, if you cut to 3 feet and you loose all your hops the plant may or may not live and you have no hops. If you don't trim it back and some how up-root it and transplant it, you may not get any cones either and the plant may or may not survive next year.
If it were me, and these were 1st year rhizomes, i would dig up as much of the root area as i could w/o trimming and hope for the best. Then i would be sure to order more rhizomes next spring in the event of the worst.