For reference (since the original discussion was from before the new Handbook), the current policy is described in GHB 18.9.3
Guidelines for the Sacrament. It is similar in language to what was stated earlier in this thread, and there is nothing exactly specifically describing what to do after the congregation is done singing, if the bread is still being broken. Any former priest will empathize with that scenario, as we all lived through it many times ourselves!
That said, what is authorized is a congregational hymn. And what is prohibited is music during the passing or after the ordinance finishes. My feelings from reading the guidance, is that additional instrumental music after the congregation finishes singing, might not meet the intent of the policy, even when well-intentioned. Your mileage may vary, and local leaders have discretion where the handbook is silent, which is always a good thing.