It looks like Dymondwood, not actionwood? Either way there shouldnt be enough flex to worry about since it really is a bunch of i beams. I am developing a new 3 piece now and I highly recommend some type of overlay across the back, I use 1/8" phenolic.
I put limbs on a handle I had clamped in a vise and pulled the limb sideways as a riser strength test, it didnt take a lot of pressure to crack it like yours is. I couldnt crack the riser with the phenolic, just the all wood ones.
And like Hitman said, it is a little narrow. I like the shape though!