The ancient and venerable folkie habit of subdividing notes to accommodate slight irregularities in meter might be of service here. (That's when the quarter note that was the pickup for "The" in the first verse becomes two eight notes for "On a" in the second verse.)
You could write a phrase in 4/4, corresponding to line type A (/ u / u). Let's say 4 quarter notes for simplicity, 1-2-3-4.
Type B (u / u /): Steal a pickup from the previous line, hold the last stressed syllable over notes 3-4.
Type C (u / / u): Steal a pickup, hold the first stressed syllable over notes 1-2.
Type Da (/ / \ u): Hold the first stressed syllable over notes 1-2, subdivide note 3 for the second and third syllables
Type Db (/ / u \): Hold the first stressed syllable over notes 1-2, subdivide note 4 for the third and fourth syllables
Type E (/ u u /): Subdivide note 2 for syllables 2 and 3, hold last syllable over notes 3-4
I wonder if this would work, or if it would just destroy the rhythmic qualities of the poetry. I will have to give it a try...