Whenever you accelerate or decellerate a subatomic particle it emits characteristic radiation. One example of this is the notorious "blue glow" from radioactive objects - Cherenekov radiation from decelerating particles. I have seen this with my own eyes in a tour of a nuclear plant and peered into their spent fuel rod storage pool (10m of water protected us from any dengerous radiation, but the blue glow was impressive).

Similarly, the act of deceleration of your protons will nececerilly involve radiation. Your figure 4 includes a "spray" of unlabelled red outputs which are presumably radiation of various types. Any "excess" energy from your relativistic protons will be converted into shockingly energetic gamma rays, so you will still need a thick frontal shield, but at least it may not ablate from proton impact, and you won't get the biologically-damaging showers of collision debris from relativistic particles. (if it works).

One issue with interparticle reactions is that they take a minimum energy to overcome repulsion forces, but they also take a minimum time. If you arrive too fast, the reaction may not take place and the impinging proton will pass by your shield almost unchanged without having time to interact properly. Only later, after it has had glancing interactions with multiple targets will it slow down enough to fully interact and be captured. This is the same as the principle of neutron moderation in nuclear reactors and thermonuclear devices, I think.

Have another box of chocs and some more sleep, and see if there's a way round this...