Using Vellum Shape Match, Pressure, and Stretch constraints (as well as some artfully keyed gravity values), I was able to achieve this cool effect of having various objects inflate but maintain their base shape. Similar to my last exercise with the pillow logo, I used an attribute transfer to affect the object to inflate after an influence shape passed over them. In this case, it was a sphere that influence the center, but its radius grew larger a bit later in the sequence to affect the other shapes.
I revisited a few tutorials from Nick Medukha, Entagma and Tim vans Helsdingen to problem solve a few hiccups I ran into.