I would never recommend a screen gain more than that of a minimal amount due to hotspotting and brightness uniformity over the width of the image. High gain screens are for rooms where light can't be controlled and you have a narrow viewing area.
A 120" width is over your typical viewing width from a 13' viewing distance. Recommended, center of theater, would be about 104" width, or closer to a 120" diagonal, not width.
Still, with the RS45 and 138" screen, you really do need the gain in some form to compensate. I'm just not sure I would go to that large of a screen with that projector, as it really isn't designed for it, and you will be compromising the design of the projector and your image quality by forcing a square peg into a round hole.
If the goal is a 138" (or so) diagonal, I just installed the Epson 5010 with a 134" Carada screen in Brilliant White (1.4 gain) in a properly treated home theater. Dark walls, dark carpet, dark ceiling. The end result was simply stunning. 2D content was extremely bright and may even need to be brought down some. 3D content was pretty much perfectly bright. Avatar showed excellent depth with good detail.
It seems like a mismatch, IMO, at this point. I'm not sure what you have right now for screen size, but the JVC isn't a powerhouse projector for larger screen sizes and, from what I've read, isn't a 3D class leader either. Both of these things stand in the way of your objective to maintain a high quality image with a larger screen size.
I LOVE JVC projectors, but while they absolutely will deliver the best image quality in 2D for the money, they operate best from 80"-120" diagonals in proper rooms. Very traditional expectations and design. Anything, including what you are hoping for, calls for a different projector first.