First off, you may want to consider changing the title to reflect that you're just talking about K-JDs. Also, for the purposes of law school admissions, "work experience" is almost always defined as full-time paid work, which K-JDs almost never have, by definition.
How many of you who went K-JD had work experience (in the form of internships/summer gigs/research assistantships) that related directly to the legal profession/business/economics/something relevant (ie not volunteering at an animal shelter or hostessing at a restaurant for some extra cash).
I'm a K-JD in what you could call a "legal internship" right now, in that I work directly under the supervision of the legal department at my office. Obviously I can't draft contracts or anything like that, but I can read proposals, write basic memos on subjects the attorneys don't feel like concerning themselves with, and do the other grunt work that I'm happy to do for free. I also have three other internships under my belt, all in DC: One in political media, one on Capitol Hill, and one in a think tank. Other K-JDs sometimes have published research in school or something along those lines, but by and large, unless they took time off before graduating, nothing a K-JD will do is all that advanced or prestigious, and that's just the way it is.
I've heard there are some schools, even in the top 14, which don't care quite as much about this stuff. Which are those?
In the T14, only Northwestern will seriously downgrade someone for being a K-JD, and that's because they have a class profile that's unique to them. Every other school is comprised of, I believe, around 30% K-JD (if I'm wrong, someone please correct me) students. It won't really matter except to the extent someone's WE is uniquely impressive. By and large, it's a numbers game and a numbers game only.
Also, would extremely high achievement in the performing arts throughout highschool and college years qualify as a decent soft?
Possibly. The strength of your softs are determined pretty much on an individual basis. Some schools may be more impressed by certain things than others would be. "Majored in Theater and acted in every play" is going to be different than "youngest person ever invited to play in the New York Philharmonic." Worth keeping in mind that something that stands out at a T14 is usually exceptional--having done things that are merely "cool" or "interesting" is pretty much par for the course--having "good" softs really means you're average, and having "typical" softs really means you're going to be weaker than most other applicants in that area.
I realize it's not a conventional one, but shouldn't it at least show I'm ambitious, driven and unique.
Everyone applying to T14 schools is ambitious, driven and unique. Everyone is unique, and anyone with the numbers to be competitive at T14s is likely to be ambitious and driven.
I guess law schools probably aren't looking for the same kind of diversity of candidates as undergrad?...
Not in a non-racial context. Again, it's mostly a numbers game.
Anybody still manage to swing a big scholarship from a t14 school simply (not that it's simple to achieve this lol) with a high GPA, great LSAT, good recommendation letters and solid personal statement?
If you have a high GPA and great LSAT by the school's standards, nothing else will really matter. If you're not in the ballpark with either, nothing else will really matter. Softs matter on the margins. So yes, if your GPA and LSAT were high enough, and your recs and PS weren't absolutely awful, you could have an empty resume and still be accepted to a great school.