Why do common-mode EMI filters lack damping networks?
You're headed for a regulatory compliance issue
The problem with jacking up Cy is that doing so increases the leakage current from the mains to your appliance's earth grounding lead.  Given that the least restrictive condition IEC(UL) 60950 permits for garden-variety devices is 3.5mA of earth leakage, this limits Cy to just under 20nF for a reasonable worst case of 240V, 60Hz power.  (If your appliance is stationary and either is hardwired to the mains, plugged in via an IEC 60309 or equivalent industrial-type plug, or has a separate earthing terminal, then you can use the relaxed 5%-of-supply-current limit provisions in IEC 60950, but those aren't intended to be readily applicable to general-purpose equipment.)