DisplayPort to HDMI is not officially supported anymore, but you should be able to find an adapter. Assuming that you can use extended desktop between the two ports (I don't have a BRIX to try out), then that would give you separate outputs (with separate resolutions) for the BRIX.
However, that still leaves the PS3. I think unless you change the Epson to a 1080p projector, you are stuck with either downgrading the output (1080i or 720p) or only using one output at a time. A switch will allow the EDID for both the Epson and the Sharp to be combined into the lowest common denominator, escentially giving you 1080i or 720p. There is no other way that would give you a picture on both.
There are a few mechanical switches out there. But most of those (usually with an LED on the switch) are actually powered by the HDMI cable. You can check the archives in this forum to see if someone had luck with one. Check under "reversable switch".