How to determine the steady state voltage across two capacitors in parallel
Just got a likely answer to my own question by asking a friend, who pointed out that charge is always conserved.

The total charge in our circuit (two capacitors in parallel) is Q = Vc1*C1 + Vc2*C2. We can then equate this to the total charge when voltage has settled, Vc*(C1+C2), giving a final expression of

Vc = (Vc1*C1 + Vc2*C2)/(C1+C2)

Sure the circuit in question doesn't have real life relevance, but I think this equation is very handy when you're just concerned with the steady state values.