Is that 1mm sheet metal all that is forming the back of the gantry?

I don't think you will get that much of an improvement using supported rail attached to that stuff, you will need to beef up the back of the gantry so that the supported rails can transfer force into gantry otherwise the supported rails will flex almost as much as the unsupported ones do at the moment.

Going to supported rail on the gantry will also mean that you will need a Z-axis mount (I think) as from the pics it looks like the bearings for your current rails are all in one block.