In all seriousness, I wonder how far removed from the original you'd have to go to be recognizable as "that birthday song" and still avoid a copyright claim? Obviously your words are different, but the subject is the same, the meter is the same, and if you stayed in the same key, all you've really done is some word play.
Maybe draw out your "day", "X's", "day", and "all" for each line into a half or dotted half note, and reverse last two notes of each line so they ascend instead of descend. That way most of the meter is preserved and it still feels familiar, but hopefully no longer infringes.