Mike,
As to how small the steps need to be to not effect your audio quality would depend on how good the power supplies are in your kit, how well do they filter out the high frequency components of the steps, and how well the non-ps circuitry deals with any remaining hf residuals that get through the power supplies.
That being said, a bunch (main cap and bypasses) of X2 caps across your hot and neutral lines would be the simplest way of removing the hf component from your ac.
Ideally, your stairstep inverter will contain its own filter: possibly a series inductor and shunt cap, or maybe just cap(s).
Can you get a look at your ac with an oscilloscope? This would allow you to see how much of the 'stairstep' remains.
FWIW
PS-PM me about getting some X2 caps if you're interested