Coincidentally, I'm in mid-paint job as we speak, and using 3M Scotch-Blue Painter's Tape for Multi-Surfaces #2090, 1-in. wide.

My knee-jerk thought was that its easy-release feature would render it unsuitable for your intended use. But, grabbed my roll, and taped 6-ft. of plastic drop cloth vertically to door trim. Actually seems to hold OK. The 2-in. wide version would, of course, give you more grab.

Note that this particular version says "medium adhesion; 14-day removal; don't use on lacquer, wallpaper or unpainted wallboard." They make, as you may know, a version for delicate surfaces – less adhesion and 60-day removal. I've used it, but didn't like it. Adhesion was too delicate.