Not necessarily. Mine was $6k because I had it built to run a turbo making 700hp+. Everything in that engine is brand new, I did not use anything over. All new hardware, new oil pump, chains, guides, tensioners, oil pan, valve covers, oil cooler and adapter, etc... I also upgraded to billet oil pump gears, ARP head studs, I then went with 03 heads/cams and a 99 intake manifold. This is all stuff you will not have to spend money on.
I personally think you could have a decent shortblock built for around $2k if you could find someone locally to do it. If you can't a majority of companies charge around $3k for a forged 4.6 aluminum shortblock. Using all of your existing components a mustang shop could probably do all the work for probably around $5k. If you went with a reman engine from ford it would probably cost around $3.5k for the new longblock, but would probably run around $5k in the long run also.
I personally would not get rid of your car, low miles and a great color. Its up to you though, take a big hit selling it or put a good chunk of money into it. I went through the same thing with my cobra 3 months after I bought. The engine developed a rattle that sounded like a power stroke diesel. Although the car was not raced and stock the previous owners did not keep up on the oil changes. Instead of taking the huge hit trading it in I decided to make some good of it and start building up the car for the future mods I was going to add.