Step 1. Create an alternative API for Reddit (I've created an MVP for this here: https://api.reddiw.com)
Step 2. Set up an alternative front-end for Reddit built on top of the alternative API (my plan is to host it at reddiw.com)
Step 3. Start implementing a custom back-end, with submissions showing up interspersed with existing Reddit content, perhaps on the very same alternative front-end to drive adoption or one on a separate URL.
How will I deal with costs/moderation? Same way as Reddit did at the beginning: text only. With images/videos hosted by imgur etc. and each thread linking directly to a separate host for images/videos.
While I do have step 1 complete and it has got some traction on Reddit I don't think any third-party app has adopted it yet. It would be nice to get that to show the demand is there. Otherwise I might not pursue the next steps.