A style of remixed music of which I've just become aware is "Bardcore," a playful attempt to re-imagine contemporary songs in a medieval style. All are limited by the fact that contemporary music is not as sophisticated as medieval music actually was; but they do have the advantage of being played on beautiful acoustic instruments and, if sung, sung by people who actually know how to sing.
You'll find a lot more if you follow this first link to YouTube. Many of them are of truly contemporary pop music, which is too terrible to sample. I'm going to pick one where the original is actually at least a little interesting. Here's a Bardcore version of an Iron Maiden tune.
Here is Iron Maiden's original.
And here, just to compare, is a random selection of medieval music. This isn't even a fair introduction; there are whole genres of this stuff, from polyphony and chant to chansons and ballads. This is a fun selection of instrumentals similar to what the Bardcore kids are trying to imitate.
UPDATE: This one's not bad.
UPDATE: A piece from 2020.