Some fun facts:
* The flux of particles in this energy regime is so low that you get about 1 per square kilometer per century, so studying them necessitates doing really wild stuff like instrumenting a patch of land the size of Rhode Island.
* These particles are so energetic that in their frame the nominally low-energy photons that comprise the cosmic microwave background appear as an impenetrable gamma ray wall thats prevents them from traveling more than about 100 million lightyears. This seems like an incredible distance but in astronomical terms this means that whatever is producing them is "nearby." We also know they don't come from our own galaxy because arrival directions don't correlate to the galactic plane.
* Current consensus says that these particles probably come from very large and active black holes in the center of certain galaxies. These objects are called active galactic nuclei (AGN).
- Would the CMB be so energetic (from the proton's frame) as to create electron-positron pairs?
- If the particle can't travel more than 100m light-years, what happens to it? Does it slow down? Get destroyed? Is the answer markedly different from our reference frame vs the particle's?
To the second question: it loses energy due to pair creation (iirc, surely simplifying due to bad memory).
I also worked in this field (Pierre Auger Observatory in the Karlsruhe group) before I "sold out" to join a tech company in late 2010. Might we have met?
Back to cosmic ray anisotropy. There was actually a big paper from the Pierre Auger collaboration in 2007 on anisotropy that made it to the cover of Science. It correlated arrival directions with a I catalog of, IIRC, AGNs. I was in my first year in the group so I didn't make the author list yet. I was quite disappointed at the time. Pretty much from the moment of publication, however, the statistical significance we got from the data started decreasing until it was no longer something we were particularly confident in. The collaboration had to publish a note on that. Ouch. We never worked out why this was happening (if other than horrible luck) before I left.
Before the publication there had been interesting internal discussions about whether to publish. The astronomers typically felt the significance was plenty by astronomy standards and we were trying to do astronomy with particles after all! The particle physicists tended to want to apply the more conservative thresholds that are common in accelerator physics. After all, what was our detector if not a giant calorimeter? :)
In a nutshell, that'll never happen. You'd have to be the unluckiest astronaut to ever live. These particles reach Earth at a rate less than 1 per century per square kilometer. So you'd have to hang out in space for like a hundred million years...
The original particle never reaches the ground. It gets annihilated in a collision some tens of kilometers up in the atmosphere.
If you were hit, I'm not sure the cascade would do significant damage before it exited your body on the other side.