I may be under-complicating this... but what's the problem with folding the end over on itself (sticky to sticky) for abour 3" and then just unroll and fold until you have enough tape? I've done this for years: unrolling isn't much of a problem, although I do have to discard the last fold where sticky-to-sticky started.

Am I missing something? I DO usually use Gaffer's tape, but have used duct tape too.