Well I got through on the regular USA number (non Skype) and the agent was able to cancel my award ticket in about five minutes. He said the taxes would be refunded "within about six days" to the original card and the miles would be redeposited to my IB account. I can see the ticket as cancelled (it no longer shows using either the IB or BA PNRs.)

Anyone have any idea how long the Avios redeposit normally takes? I should have asked but forgot to do so.