Could I substitute the heavy cream and sugar for sweetened condensed milk?

You’d definitely want to cut down the sugar inside the recipe - the more equal substitute would be evaporated milk (unsweetened)!

Stella Parks has a recipe for homemade sweetened condensed milk here: https://www.seriouseats.com/2017/10/how-to-make-sweetened-condensed-milk.html. My guess is that you could replace it with heavy cream + sugar, but the filling would probably be runnier.