What most people do is swap in a WRX turbo engine (and all related bits), wiring, and ECU. The '02-'05 are usually the most cost effective. This has been done hundreds of times. All Subaru engines from '90-2010 were EJ-based (or similar) and share engine mounts.....that's the least of your worries.
Note: I wouldn't buy a used Subaru turbo engine of any model (maybe an EJ22T, but those are exceedingly rare and not easily compatible w/yours)...they're not known for their reliability and you never really know how well maintained or abused they might be.
NONE of these will maintain your MPG....but if you do go w/a full swap you can get a custom tune which may help w/the economy.
If you haven't already read about the WRX swap, then it's time to start your Search. MANY other Subaru sites have this info readily avl. - RS25.com and NASIOC.com are two common sites. Beware, READ UP and get informed before asking questions, as those sites are not kind to those that need a spoon-feeding.
Note: Your '03 OB uses 99% the same engine and electronics as the Impreza, Forester, and Legacy - NON-turbo versions, so that's why the other sites are relevant.
For the sake of "cheap" power, there exists an LS V8 swap kit for the BE/BH platform (your Outback). It can be modified for your choice of matching transmission, but the whole kit is not exactly cheap. Let alone the wiring nor the rest of the drivetrain (rear diff, driveshaft, axles, etc).
Your easiest route is to sell your OBW and get a H6 version available in the same year range.