you bring up some interesting points, very interesting indeed.
really the whole idea comes down to balance, that is when you talk about arrangement and what's considered a remix. how much of the original is left in versus how much change/addition.
if you want to do something that's twelve-tone, go for it, just make sure you have the right balance of materials. for example, i might think of including tonal or modal material that includes the original stuff from the song being remixed and then have a sorta "B" section with new original material that could be twelve-tone material if you choosed it to be.
my opinion on the twelve-tone idea: it may not be a great idea to use a row to create something new with a melody from a video game track to base your remix on...simply because it might not be easily recognizable. though that really depends on how you'd be arranging your row and how you'd be using the rhythms and other elements that go with it, etc.
as far as a broader spectrum of styles/genres...sure i'd like to see all kinds of types of them here. i doubt many would be in the styles that you mentioned because not many people who are involved in this community could write something that could be considered Palestrina-like counterpoint or something that could be considered twelve-tone. i'm sure there's some talented people out there who could...that also poses the question of, would anyone really do it? i think the answer really is that if it sounds good...do it.