I don't think a simple rule (like the HCA) applies to step cuts. You would need to model each stone in all detail to get some reliable result.
If the stone's optics are not your concern, than you will find different sets of numbers which all make useful, but not complete descriptions of a standard. There is no "ideal" set agreed upon, as is (nearly) the case for rounds.
By reputation, the historic Asscher cut is a deep ( roughly 70%-80%) cut with a tiny table (say...40%-55%) and a high crown.
The table and depth range for the Royal Asscher was mentioned on an older thread (which I failed to find). As far as I remember, the numbers are in the neighborhood of 50% table and 70% depth (which implies crown height about 20%), but I hope you could find the original source for these. Obviously, there is much more to the RA than table and depth!
Generic "Asschers" come in all flavors and the standard for emerald cuts would apply to judge them. Using the AGA tables, you might want to consider the range of parameters with the smaller table for each cut grade - given the "traditional look" of the cut which does imply this. Judging from the look of generic square emerald cuts, I would set the max for table at 60% and look for the set of proportions of the 1A-2B AGA classes as a good range to start with - if you must go by the number up to some point (and online this is such a huge temptation! - if we share the same impression at all, that is).