Would the "baseball" even slowdown appreciably from the nuclear explosions?
An "explosion" is really an event on the short end of the human timescale. But events around that ball are happening on a nanosecond timescale - they are fusion reactions, not explosions.
But I think Randall might have missed an important bit. He's treating the baseball as too solid.
Let us think from the ball's point of view for a moment. The ball thinks there's a bunch of air moving at it at 0.9c! In essence, the ball experiences what is effectively a very high energy particle/cosmic ray beam the density of Earth air!
Cosmic rays mostly pass through normal matter, which is mostly empty space, after all. A typical cosmic ray can pass through a couple inches of solid gold - a couple of inches of baseball are not as much an issue.
When they do interact, they most frequently kick electrons off atoms as they pass by, and ionize the matter. Only very rarely does a cosmic ray yield a full nuclear reaction (the nucleus is a tiny target to hit). And that doesn't only happen at the surface - the ray particle will pass through some thickness before it hits something directly enough to interact, possibly passing through without interacting at all. All those interactions will happen throughout the body of the baseball, not only at the leading surface.
Moreover, nuclear fusion might be suppressed, because the encounter speed/energy is too high - fusion happens when nuclei collide and
stick to each other in deuterium fusion, the particles are moving somewhere around 0.1c. If the interaction speed/energy is too high, they don't stick, they plow through each other, breaking each other apart - the result is more like fission.