Pseudonymous:
"...suppose you have in front of you a ballad sheet with no tune on it. It might not be written in a regular metre... You try to fit it to a tune you know, and end up with something lacking rhythm, or where the emphasis of the tune falls on words that aren't naturally stressed in spoken English. You also end up having to change the tune when there are more words than your original tune has notes for."

Firstly, the ballad you mentioned (Roud V2800) is a blackletter broadside from the mid-17th century, although it does seem to have been printed up until at least 1800 in unaltered from (interesting to see some illustrative woodcuts that actually reflect the content of the ballad, by the way!). Steve Gardham knows far more about this than me, but my experience is that texts from this early period were invariably long and wordy, and actually quite hard to sing - the evidence that anyone actually sang them in that form is scanty. The broadside texts that correspond most closely with collected folksongs (Henry Martin, or Sweet Primroses, to use two examples already discussed) were much later - probably the first half of the 19th century - and far shorter and less verbose.

The second thing to say is that traditional singers were pretty good at fitting lyrics to tunes, amending texts if necessary. My old friend Gordon Tyrrall wrote a dissertation many years ago which compared the texts of songs in the Copper Family's repertoire with the corresponding broadsides, and found that the songs as sung by the Coppers had had a lot of awkward edges knocked off to make them more singable. The other thing that can be done is to lengthen certain words if the text is too short to fit the melody line, or insert extra syllables into words if there are too many notes in the melody. Joseph Taylor did the latter: "Poacher bold as I uddenfold", and so on. But, if push came to shove, and the text had too many words to fit into the tune, singers would sometimes simply lengthen the line as much as necessaryto accommodate all the words. There's no problem doing that if you don't have a rhythmic accompaniment.

I've set more than a few broadsides (including some 'unsingable' ones!) to existing or new tunes in the past. For what it's worth, if I was forced to perform your St George ballad, I could make it fit a tune I wrote very recently in 4:4 for a 19th century Chartist song, by lingering on certain words, or inserting an extra one where there are too few to fit the line, or by squeezing in a word before the first beat.

The opening lines:
"Why should we boast of Arthur and his knights
Knowing how many men have performed fights"

...are particularly clunky, but you might get around the problem of the stresses in line 2 by squeezing in the 'knowing' ahead of the beat - so the first-beat stress falls on how, then singing per-form-ed as three syllables to fill the gap. If it were me I'd be more radical and edit it to something like "When so many other heroes / have fought for what is right..." [stresses underlined]. There's always a way.