Paul,
I tried to do that with some carbon fiber from the back, but couldn't get my hand in far enough. Just made some plywood 1/2 formers 7" and 14" back from the wing tube mount. Wanted to make the belly strong enough to pick up the plane. Only time the sides are an issue for me, is when I'm trying to turn the fuse upside down to work on it. Hasn't been an issue otherwise. But if your cockpit tub is out, you should be able to get some bracing in there pretty easy. I'd put some support in the belly while your at it.
The only other thing I'd suggest, is to shape some styrofoam and glue it into the top half of the vertical stab so you can pick tail up when walking the plane around at the field. Just my 2 cents.