I think I'd start by subbing light cream for the heavy. Using stock would probably taste great, but it would definitely alter the flavor profile the creator of the recipe intended.

Eight cups heavy cream? Wow. I'd sub in either milk thickened with a little cornstarch or flour; some cottage cheese or ricotta (being careful when heating so it doesn't curdle), or the old standby, evaporated skim milk.

For what it's worth, it does say the recipe serves 12, so it's only 2/3rds of a cup of cream per person.

Perhaps half stock, half cream?