Nice map. I prefer square grids for dungeons myself, but hey, it's whatever you're used to.

Have you tried exporting the map to PS or GIMP, creating your grid as a pattern, then creating a new pattern fill layer using the grid with a multiply blend mode, inverting it and painting it on only the room floors? You can mess about with the opacity and stuff to achieve the level of visibility you want if you use this method. Great 'trick' I picked up from Butch Curry's Fantasy Cartography tutorials.