I think it's important to remember that Unfinished Tales is Unfinished - as with the Silmarillion and material found in HoME, we have texts which had not been completed and passed for publication by JRRT. It's down to speculation what changes he might have made during the completion of these stories (for consistency or otherwise), had he finished them himself. So the picture is less tidy (and more interesting) than if we only had the material published by Tolkien during his lifetime.
With Tolkien of course we do have a lot of material to work upon, lovingly assembled into HoME, and other posthumous publications. So it is an odd situation. A sort of hierarchy probably presents - you might hold that:
What Tolkien wrote and published himself is more canonical than unfinished published works.
Anything written by JRRT is more canonical than stuff written by someone else...
Though of course that is disputable: if more people have seen the films than have read the books, or if more people prefer an aspect of the film version, does that become, in a way, more canonical? (I presume that would be what would happen in a tale which spent time in oral tradition before variants were collected and studied - a sort of Darwinistic process would be going on, the more popular ideas being the ones likely to be retained in future tellings).
Prof Tom Shippey has an interesting argument about this in his book The Road To Middle-earth. He notes that the effect we're left with is something quite like the situation in the traditional tales with were part of Tolkien's inspiration. Shippey's idea (as I understand it) is not that Tolkien created this effect deliberately, but that he might not be displeased that this is what we are in fact left with. Stories such as Sir Gawain, Shippey points out, have passed through many minds, tongues and pens: so multiple and sometimes contradictory versions exist. Plot details and character motives (stated or implied) can move around. Shippey has an example involving a story of Brunhilde; but I have lent the book, and don't remember the details (and similarly, if I have mis-presented Prof Shippey's idea because of having to do this from memory, please do chip in & say so, if you know more!)
As an example I know better, I can offer you Tam Lin, a story from the English-Scots borders, which is known in multiple versions (Childs alone collected 14 variants). Sadly, I can't now find a web page which tabulates a lot of these. But here is a flavour of the "usual" plot and its variations. I think it will provide a good example to compare with the Tolkien situation.
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So - Tam Lin and his variants:
Core: Janet, a noble maiden, is warned not to visit Carter-haugh, because the faeries are occupying it, and exacting tribute from any visitors. But Janet says that this land is hers by right and goes there.
Variants: Different details of what the tribute might be, and whether it is possibly going to be (or very likely to be) her virginity. Some versions have Janet acting in ways that are likely to be provoking to the faeries (wearing green, plucking plants, plucking a rose specifically). The audience can gather different inferences about whether Janet is a foolish girl to ignore sensible anti-faery precautions, or is doing these things as a deliberate challenge.
Core: Tam Lin appears, and takes Janet to Faerie. On her return, she discovers she is pregnant.
Variants: various inferences as to whether Janet has been abducted and raped, or whether she and Tam are willing lovers.
Core: At Janet's castle, folk are aghast at Janet's pregnancy. She sets out again to Carter-haugh
Variants: In several versions Janet gives a robust defence. The possibility of a herbally induced abortion is usually mentioned. Differing statements and inferences about whether Janet is determined not to do this, is considering it, or plans it. Does she go to Carter-haugh to try and meet Tam again, or to collect abortifacients?
Core: At Carter-haugh, Janet and Tam meet again. She discovers that he is a mortal man, held prisoner by the faeries. He tells her of a way in which she can rescue him, after which they will marry. She must ambush a procession in which he will be riding, drag him from his horse and hold on to him, despite the changes in form he will then magically undergo.
Variants: Information on Tam's background, including details making him a highly eligible husband. Tam offers Janet this way forward as an alternative to abortion; or she extracts some or all of the necessary information from him by the "correct" questions.
Core: Janet ambushes the procession, and successfully drags Tam from his horse, holds on to him through several magical transformations, and so wins him as her husband.
Variants: The faery queen either rages at Tam for having tricked her, or congratulates Janet (for her bravery, or for the excellent match she has made).
I think this is a good example for the way that stated or implied character motivation moves around. One imagines that the details of sex and abortions were too much for some storytellers (or audiences), whereas others might have wanted to turn this into a moral tale about ladies venturing out unprotected. Some versions make less sense than others, perhaps because of omitting details which can be found in other versions. Overall interpretations therefore vary hugely - in the bleak corner, one can imagine that Tam cynically engineers the whole thing so as to use Janet as a means of escape, and will dump her shortly after the credits finish rolling. But I much prefer it as a story of a brave and resourceful protagonist who stands up for herself and rescues her lover.
I used "core" in the above plot outline to indicate features which are always or nearly always there. But there are no rules (except that boring or incompetent stories tend to get either mocked or ignored). Someone wanting to write a variant now can do so; either holding with the "core" or deliberately pushing against it (e.g. one could write a version in which the Faery Queen is the wronged party, with predatory Janet seducing & making off with her lover...
The original version of Tam Lin is now well lost from the Tree of Tales - those leaves have long since blown away, but the branch remains hale and each spring it puts forth stories anew. Shippey, with his Brunhilde example, suggests that the original story might be reconstructed by a sort of philological or phylogenetic method. Myself, I'm not so sure that's either possible or desirable: it seems a bit like the simplistic search for a "missing link" fossil - something that would be conveniently part man part ape. I imagine that if we could magically recapture every variant of a story such as Tam Lin, we'd find a very complex patter of mutation and interbreeding. Nor, of course is there any guarantee that the earlier versions would be "truer" or even better as stories.