I've been using an Aeropress for years, but had never heard of the inverted method until this thread (obvs, I don't hang out in coffee communities much...)
So I tried it, and while I will say it was night-and-day different, I prefer the standard method. The inverted method just loses the two attributes that I value most from the Aeropress: it was grittier and more bitter than the standard method.
Now, granted my preferences are not everyone's, and I'll be the first to admit that I might just have a plebe's palette when it comes to coffee, but I like the clean, sweeter taste that I get with the standard Aeropress including the paper filter.
I will say that one of the sources suggesting rinsing the paper filter is a good tip, and one that I never considered, even though I'm a chemist on my day job (though I don't think it makes too much difference, given the screw-on feature means the paper isn't going to move, wet or dry)