They'd both work OK.   But a hymn tune seems to fit better, and more likely if he ever did sing it, since those seems to habve been the kind of tunes they used (cf Oh What a Lovely War).

Quite a lot would fit, but "Aurelia", the tune used for "The Church's One Foundation" (among others) is the one most widely known, and seems to work well with the words.

(The line "And to think that I am missing them, makes me exceedingly glad" fits better amended to "And to think that I am missing them, makes my heart feel glad.")