I think we may have found the solution!!! I can't begin to tell you ladies how incredibly relieved I am that things are going so well!
We had a no nap day today (large commercial vacuum truck to clean the neighbour's carpets started up as I was changing her bum and putting her into her sleepsack - of course, right outside her window!). Went to the mall hoping for a stroller nap - nope. But since she did stay awake, I was able to be certain that she had NO reaction whatsoever to the milk that she had finished moments before said truck busted our nap time!
I am going to actively transition right off formula and onto lactose free cow's milk in the next couple of weeks! Now, off to buy a special sippy for milk only (thanks for the idea Laura!)...