Try ballads such as Tam Lin and The Twa Magicians.
One theory that I came across is that these are perhaps based on initiatory ceremonies from the dim and distant past - much the same as the shamanic transformation process that you mention. I'm sure that there are others. (I put one together myself based around the myth of the birth of Taliesin which I found interesting because, in his case, it is the male who is fleeing and initiating the transformation sequence.)
By the way, I once came across a theory that the Outlandish Knight could also have been a merman of some description who wanted not to drown the lady but carry her to his undersea kingdom. Apparently the talking bird ("parrot") is often a sign that the ballad is a "magical" one and it would explain the lady's reluctance to let her father know what was going on.