OP: What happened with JEE? Sorry I haven't completely followed the thread.
What are you interested in, engineering or drawing, or a bit of both? Each field requires different aptitudes. If unsure, then do what everyone does, go for engg.
Did you try for B.Design and B.Arch courses in IITs?
Your AIEEE rank won't fetch any good college seat. :/
VIT is a great place as far as accommodation is concerned, and a few friends/acquaintances of mine who are from North that went there adjusted to it. The placement I hear is rather good there (Facebook took 3 people from there(!)). So don't rule it out completely.
Manipal is a place where all the academically disinterested friends of mine ended up. I don't mean to disparage or anything, just that that's what happened. The place itself is picturesque, and rich folks from all around come there. It's easy to get waylaid there.
Did you give DCE/NSIT CEE?
I really feel bad about the BITS thing, did you try asking them for some feedback on the issue (from what I read, their FAQ was updated rather late...you could ask for some leniency/alternatives with that score. Slim chances, but can't hurt).
All the best with your admission man. FWIW, I've completed engg. and I'm still hella confused what happens next.