Hi, recent fiction grad here.
You're right that many schools have a literary preference, but the best writers will get in somewhere regardless of form. You also see a lot of the newer literary big shots toeing the line - Ben Percy, George Saunders, Karen Russell etc. If it's hard genre, you'll have a more difficult time, but an original story, written well, with elements thriller, mystery, and horror, would be well received at most programs. (Brown, as you mentioned, is its own animal.) While the article has some good points (I do think the literary / genre divide is artificial and silly) I don't agree that MFAs push a pretentious echo chamber... not the ones worth going to, anyway. It's also holding up Flannery O'Connor as the main voice it's pushing against, and she was referring to what workshop looked like in the 1950's. For a view on a current day workshop atmosphere, check out this essay: https://www.buzzfeed.com/alexanderchee/my-parade
As to where to apply, because you're more of a genre person, program fit is going to be especially important. Even if you got into an excellent literary program, the faculty there aren't necessarily going to be equipped to be most helpful to you. My advice is to look up your favorite authors and see if they're teaching anywhere, make a list of those schools, see which ones are funded, and narrow it down from there.
It's not unreasonable to ask for 6-8 recommendations. 10's a lot, but if you have a good relationship, go for it. If they have creative writing backgrounds you may also want to think about asking them for suggestions, it gets them more invested and makes it less of a chore. Make it as easy as possible for them, thank them profusely, and keep them updated if/where you get in!
Edit: Forgot to add my big note. Don't get discouraged, and don't be too nervous to apply! It's really impossible to guess which schools are looking for what style of writer on any given year, so worry more about what you're looking for in a school than what they're looking for in their applicants. Good luck!