the approach advocated by private_messaging as "the best way"

What? There is no mention of this anywhere. I have no idea what you're referring to with this phrase.

I'm not going to provide an alternative because it doesn't matter. Using the alternate formulation where you count every padded program with the same results as being unique, you get the same results, with the addition of another underlying assumption. By assuming they do not count as the same, I (am attempting to) force potential objections to confront the actual basis for the argument.

So go ahead, if you like. Treat those as distinct and work out the consequences. You'll reach precisely the same conclusions.