Still humming.

humming frantically (true)...don't like this...
humming crazily (true)...
humming non-stop (not in tune, but true)!

humming gently (false, I wish)...
humming beautifully (false, I wish)...
humming softly (oh, I've got it!)

Here you are, the amended lyrics.

auntie judy humming softly
to the tune of 小(小)姑娘

miss the dumplings made by rafa's
amazing papa in beijing