The advantage of using the Aligner clamp on the balsa strop is consistency, from pass-to-pass. It eliminates the variability in angle, which inevitably rounds off an edge. Even if the set angle won't be exactly the same as with the Aligner's hones (due to differences in thickness, and the slightly different manner of using the clamp with the balsa strop), just maintaining a consistent angle will produce good or even excellent results. I just 'eye-balled' the angle with my Aligner clamp on the balsa, just to make sure the edge itself was flush to the strop (a magnifier helps with this, in the setup). If the angle is too low, you'll just miss the edge, without harming it. If the angle is perfectly flush on the bevel, fantastic. And if it's slightly elevated, then you're effectively 'stropping' a very consistent micro bevel on it. Still very good, so long as the pressure is maintained very light.
You can use the clamp's angle-adjusting arms, combined with 'shimming' under your balsa block, if need be, to get the edge flush (or nearly so) on the balsa. An easy and very finely-adjustable way to 'shim' the block would be to stack paper under it. Just add or remove sheets to adjust the height of the shim.