The experiment is completed. Can Crossword Solver handle a puzzle with an unconventional numbering scheme? Via the masterful work of Will I. Johnston, the upshot is that, yes, indeed, it can.
I wrote the first version of this grid quite a few months ago after listening to a Ryan and Brian podcast. It's gone through several re-writes, mainly because the seed entries were awfully stingy with the fill possibilities. Will tweaked the seed entries which, thankfully, made the building effort much smoother.
There is a special clue category available in the lower half of the applet's right sidebar, while the Across and Down clues are living together like cats and dogs in the upper half. The highlighting of the appropriate Across and Down clues was a bit touch and go as I was solving. But each of those clues appears above the grid as you solve, just as they do in Across Lite, so that's no major setback.
Other than that, no spoilers in this post.
The Crossword Solver program is, of course, available free of charge at http://www.crosswordsolver.info/