I don't think that I'd try a repair until the I understood the cause of failure and even then I'm not sure I'd trust a repair done at a point that failed. The big problem that I see is that you can't stagger the scarfs of the wood strips, so now you'd have a two scarf joints at the failure point.

In the first picture, is the dark line running from the leading to trailing edge a couple inches below the end of the web a scarf joint? Also, in picture 3, it looks like there is another dark line running from leading to trailing edge on the upper side just below the break.

"...the forces were transmitted up the mast to the first weakest point."

It doesn't work that way. The vast majority of the boom compressive force is taken up by the mast step. If the force from the boom is 100lbs, the mast is 36ft long and the gooseneck is 1ft above the step, then 97lbs of the load is transmitted to the mast step.