As covered above, you will not economically turn a WRX into an STI.
On the hawks the engine internals are different (supposed to be stronger!), different turbo, injectors, map, exhaust, suspension, wheels, brakes, gearbox (very close ratio box and really nice/acurate to use), DCCD, dials (they are backlit LED and sweep on start up

), seats, body styling including spoiler, front winglets, side mouldings and so it goes on. And of course when you come to sell, an STI is an STI and an STI'd WRX is still a WRX on the log book at least, so the values differ. A complete false economy imo.
That said, your 350bhp WRX must make for a very nice quick road car.
I went from a 2004 WRX (blob) to a 2006 STI (hawk). Both fantastic cars in different ways, but very different. The blob was easier to live with day to day and the hawk definitely more fun. I was lucky, I had no problems with the 2.5 unit in the 6 years I owned it and for the last couple of years I had it it was mapped to 350bhp with 390ftlbs so was rapid. Sold the hawk in 2012 (shouldn't have

) and since have had a 2005 STI Blob. The 2.0 in the blob felt stronger, was more fun in that all the power arrived in one big hit, but the hawk was definately the quicker point to point car with all that torque.
If I was doing it again now, it would be an RB320 for me, or one of the very last STI's before the hatch. Granted the JDM cars are 'better' but part of Subaru ownership for me is the flat four burble, which the JDM's don't do (though they scream nicely!)
Steve