"Play the music....whatever it is.."
Can't disagree with this in any way, if that's all you wish to do, if you wan't to take it further it becomes more complicated.
If it hadn't been for those who wanted to take it further - the often non-performer researchers, collectors and enthusiasts , et al who made the songs available to us in the first place and have continued to do so, we wouldn't have the songs we have at our fingertips nowadays and we certainly wouldn't be aware of each others existence in order to exchange ideas on forums like this one.   
I've set out my own stall for what my involvement is - not everyone's bag, but whenever I get the opportunity I'm happy to become involved in sharing ideas and experiences.
It certainly has kept me from being bored and given me massses of pleasure over the last half century and has made me a lot of friends along the way.
"trying to define the (almost) undefinable"
It's only undefinable if you ignore the definitions as they exist and try to make sense of them - works as a rule-of-thumb for many of us, though they are in need of refining.
The point always ignored is that many of the older singers who gave us these songs had their own definitions for the songs we call folk songs.
Walter Pardon, probably one of the most important English singers in the latter half of the 20th century, called them folk songs, a term he possibly picked up from the use made of Sharp's 'Folk Songs for Schools' when he was a child.
He probably associated the songs he was taught then with his family's large repertoire of songs and spotted the link.
When he carefully wrote down all his family's songs he could put together in an exercise book in the 1940s, they stood on their own - virtually all folk songs.
He filled several tapes talking about the differences between them and his large repertoire of music hall songs and Victorian Parlour ballads, which he had in abundance and also sang, when requested to do so, though, to my recollection, he never did so at a folk club.
He told us of the time when relatives of his own age abandoned the family repertoire and took up "the new stuff" - a clean break with "the old folk songs".
Blind Travelling woman, Mary Delaney had a repertoire of somewhere between 150 and 200 folk songs (we never managed to quite finish recording her), which she referred to as "my daddies songs' - when we recorded him, he managed to remember around half-a-dozen, she was referring to the TYPE of songs her father sang.
She could have doubled her recorded repertoire with the Country and Western songs she knew, but refused point-blank to sing them because "they aren't the songs we're talking about".
She said she only sang C&W because, "They're the type of songs the lads ask for when we're all in the pub".         
Among the rural Irish singers, they call them "traditional, sean-nós, old, come-all-yes", a few call them folk.
Virtually all identified them as "Norfolk" or "Taveller" or "Clare"...., wherever they might have originated - they claimed them as their own.
Many of them expressed strong opinions of how they should be sung, we are now recording a ninety-odd year old singer who actually stopped singer his magnificent repertoire because of what "the young crowd are doing with the songs".
It seems that the 'anything goes - near enough for folk song' approach is a 'folkie' rather than a 'folk' point-of-view.
Maybe that's a clue to a new name for what happens in many folk clubs nowadays, 'folkie songs' - certain would help me decide what tin to open.
"Peter Bellamy used the term 'Tradition Idiom'"
That's not a bad term to use to discriminate between the imitations and the real thing - I agree entirely that Peter was one singer who was well aware of the difference.
"maintaining a tradition"
Maintaining a tradition is fine, using traditional forms to create new songs is a wonderful way of doing that, but for me, if we are going to make use of all the other information that our contact with folk songs has brought with it, it is essential to establish the difference, hence these endless discussions.
I cant begin to describe the amount of new knowledge I have gained over the last year by having to annotate the songs we have collected in County Clare in the last forty years - it's thrown open a load of doors into this area's social and political history since The Famine - 'The Half Crown', 'The Cattle Drive protests', ' The West Clare Railway', 'the sinking of The Leon', 'The Quilty Burning', 'The Fanore School incident', 'The Buckingham Palace Meeting'.... dozes more historical and social events that would have been buried in time if they hadn't been immortalised in songs.
As I say, maybe not your bag, but enough to put enough petrol in my tank for a few years to come.
I suspect that I'm not alone in this.   
Jim Carroll