So I dug down deep and tried some paper matches - came with some MRE's a fairly long time ago. While better than the strike anywheres, they didn't last long enough to fuse a thin 1/2" nylon strap.
FWIW, one trick with paper matches: use two at a time, and tear them all the way down through the base (where the staple is). Burns longer and hotter.
Still hard to beat a mini-Bic in your pocket though.