You probably could, but as said you would be in for ALOT of modding to make it work.
There isn't a whole lot of extra room in the 300, so I doubt that you could fit a 2nd normal sized PSU in it. Even if you could, cable management would be a little insane. But as others have stated you could try a 5.25'' Bay style PSU.
As far as a GTX295, it will fit, but you may have to angle it into the HDD cage before you try and seat it in the PCI-e slot. You may also have to rearrange your HDDs as well depending on how many you have and where you have them placed.
There are external power supplies that are available from online vendors. Just do a search in Google.