Well gentlemen, I proved my hypothesis, that if I can't shave my jaw-area, it's because my razor's dull.
I sharpened up my straight-razor, stropped it to within an inch of its life and with hot lather, went to town on my face.
Two good strokes and I got my right under-jaw area nice and smooth.
Yes, a proper shave ready blade will certainly help in this area (or any area for that matter ), but don't forget that proper technique is just as important. You'd be surprised what a good scything stroke will do for you, even if that blade isn't exactly scalpel sharp.