I seem to remember that aside from the continuous drum beat, the funeral dirge was the only music played during JFK's procession. The Navy Hymn (Eternal Father, Strong To Save ...) is very moving and was certainly appropriate for JFK.
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If I'm not mistaken, the Navy Hymn was played at the foot of some steps, probably as the casket arrived or departed the Capitol. Jackie Kennedy was so atuned to the historical significance of those solemn days, so aware of every detail of protocol and yet determined to personalize it for her husband's memory. She selected the Navy Hymn to signify his military service and I'm almost positive there was bagpipe music at Arlington in honor of his Irish heritage.