There are wrecked 04 stis out there for around 7k?!? I have never found one.
Keep an eye out on craigslist for a wrecked one, if you still decide you want to go through with it. If you have a friend with a trailer and don't mind doing a weekend trip you will have a lot more success at finding one, possibly in Oregon or Socal. Last time I checked a wrecked, fair mileage (around 50k mi) 04 sti could be had for about $10k. In my opinion, doing it under $10k would be difficult unless you stumbled on a great deal.
The insurance I haven't had any issues with, as technically in my case the parts were all out of a newer wrx
and since mine already had a turbo and such they didn't make a big deal out of it. As far as registration and DMV, I've been told that as long as it will still pass smog and the engine is out of a newer model car you will be ok, you can never put an older engine into a newer car. I would give them a call just to verify.
And Dean is definitely right about never seeing a return on your investment.