Hi Holly, I'm in the UK and tune "birdcage" overdamper action pianos all the time. There are scores of thousnads of 'em! Regarding mutes, I find it best to use a Papps wedge, easily inserted between the damper wires. You quickly get into the technique of feeling for the strings with the tip of the wedge. The rest is common sense. I;m sure you'll soon find out why one note "keeps ringing" - sticking damper flange center, bent damper wire, damper head come off etc. Hope all goes well. Best regards, David Boyce.
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