Do a straight 3L swap.
Probably do that for under 2k and still refresh everything. Then drop a turbo kit on that. That's 7k. Close to your price range.
Heck folks have done a 3L swap for under 1k before...
Even if you go hardcore NA 3L you'd be hard pressed spending more than 4k IMO. (Parts & machine work) Well if you did your homework anyway... I can easily see you wasting tons of money when you look at place like SHOShop selling a 3L shortblock for 2k
250FWHP is definitely attainable. My choice would be the SVT cams with adjustable gears.