I used to have one of these, and you have a few options depending on what you really want, I didn't like the big gap as I felt the plane buckle a little on my stand.
So easy option, go to Hobby Lobby and get a $1.25 peace of 1/4 in hard wood square dowel and cut it to length from former to former and epoxy 2 of them about 2 in apart running from front to rear former. This is what I did and was great!
Option 2, I have some really heavy weight carbon fiber tow, with this you will need to layer it up about 5 3-4 times and run it just like the wood dowels.
Option 3, Put a 2in strip of 6 oz carbon fiber strip down the center.
Option 4, There is foam epoxy base foam that will stiffen, but will not help for what you want to do.