If it is such a good blackberry, don't risk losing it. Take literally dozens of cuttings. The ones at the end of the one year old growth will root better, and why don't you try some with hormone powder and some without? I would make up a equal mix of clayey soil, potting compost and grit, in deep pots. Cuttings at least 9" long, and cut below a bud and get as many buds below the soil surface as you can. Keep moist and hope. The other thing you could do, is peg some tips of stems into the soil in an unobtrusive place and ask the people who are moving in to let you come back in the summer and dig them up (they should have rooted). Also, ask them if they intend to dig it up and dispose of it (people do that type of thing!) to give you a ring so you can go and rescue it. I would also try to dig up at least some root now, with stems attached - they do take a lot of abuse, you might be lucky.