I think it's important to draw distinctions between a literature search, Arts and Sciences, performance, and research. I look at them this way:
A literature search is going to the library and reading a lot about medieval music, poetry and performance. You can document the results of a literature search without ever singing a note.
Doing A&S would be, for a performing artist, creating and rehearsing a performance. This performance might be based on the results of a literature search or it might not be. It might someday get performed in public or it might not. The process of developing a performance - whether or not it's based on a literature search - can also be documented.
A performance is getting up in public and singing/dancing/reciting/storytelling/whatevering. I'm having a hard time thinking of a performance that wouldn't have some kind of A&S process behind it - even an entirely spontaneous improvisation has the knowledge of how to improvise behind it. The performance itself is not usually documented, no more than a dress has its pedigree sewn onto its sleeve.
Research is what happens when you do all of these things in an attempt to learn more about medieval performance. You do a literature search to see what "the authorities" think about medieval performance, you develop your own performance, and then you see how well it is received by your audience. If they hated it, that will affect how you do your next performance.
I think it's also important to distinguish between regular performance and performance for competition. I like to use clothing analogies for this. Everyone in the SCA needs to wear clothes, and they need to be vaguely medievaloid clothes. I'm not a clothes guru myself, so I wear things that are (usually)... okay. Sometimes I even break out the "barbarian" raggy leather tunic, which is so wrong. I do not even think about entering these things into an A&S competition!
For the purposes of making music, entertaining others, or transporting them to the Middle Ages in their minds, all one needs is "SCA appropriate" music. That's fine. But if you want to take that research-y, A&S approach to it, that's not fine.
That said, not all A&S competitions are the same, and that goes double for the performing arts. I can agree or disagree with what a judge thinks is important, but I fully support a host's right to establish whatever rules and standards he or she wants to use for a competition. If I don't like it, I don't have to compete. (I would stipulate that standards should be published well in advance of an event. Preferably, the judging sheets should be made available.)
What do I think is important? I would like to see more scholarship (in competitions). Not everyone who makes great garb enters it into A&S competitions - a great performer who isn't into research possibly shouldn't feel badly about not entering research competitions. But the final product needs to be effective, too - the actual performance counts. Emotional intensity, technical ability, and attempted difficulty (I'd like to be able to give points to someone who tried something hard and fell a little short, as opposed to mastering something simpler) ought to count.
That's for a traditional A&S, for performance. I think themed competitions, or challenges, or whatever you'd like to call them, would be a lot of fun too. There is no reason you can't have competitions that strictly challenge the performer's ability to, well, perform. I'd say it's not A&S (research, really, but the SCA says "A&S" when it means "research" most of the time), but it's a perfectly valid idea for a fun competition at an event.