Ah, that’s probably a better process than our house’s trick of having two separate MA EZPass accounts simultaneously associated with the same car in order to get a second transponder I can use when I rent. (Our way makes it hard to predict which account gets billed in the rare occasion that they have to fall back to the license plate because a transponder read for the double-associated car fails.)
My sample size is not huge, but personally I’ve never had a problem with associating mine with a rental using the timestamps of my rental contract and indicating that the car is a rental.
Tiny typo: Indiana is IN, not IA. (Apparently there once was a Bloomington in Iowa, but that now-uninhabited locale was neither on your itinerary nor plausibly ever <7 hours of legal driving from Pittsburgh PA.)