Bill Houghton, Sebastopol, CA
and I haven't tried it myself*, but: I've seen pictures of guys who clamped the saw blade down on a shim of appropriate thickness on a large flat surface - say, a table saw or the dining room table (probably best not to try this latter approach at home, unless you have no significant other or s/he is very tolerant) - then run the handle back and forth on the same flat surface. Or perhaps vice versa - clamp the handle down and run the sawblade back and forth while it (the blade) is resting on the appropriately-thick shim.

You've got very little depth of cut with those blades, so you might be able just to start the cut before the shim interferes, finishing it off using Patrick's method.

*...although I have used much the same approach (along with legions of remodelers) for undercutting existing door trim (casing, jamb) when putting in a new floor that's thicker than the old one: put a saw on a piece of the new flooring and use it to undercut the trim.