I believe I may have seen the revised formula used in an attribution presentation (I believe it was IRR attribution by Dr. Stefan Illmer).

However, portfolio values generally do not match the index values. Unless the underline values (or data) that go into the revised formula is adjusted to start off with identical numbers, it'll probably double (or more) the effort just to calculate excess return.

It might be better to use what Andre or David had stated. A more interesting topic is on attribution analysis. I'm surprised no one wrote about my error.