The galactic magnetic field is fairly irregular on distance scales that are small compared to the size of the galaxy (although there does appear to be structure to the magnetic field associated with the spiral arms). In a uniform magnetic field, a charged particle would follow a nice spiral trajectory. In an uneven and varying magnetic field, charged particle trajectories become rather more erratic since they are, after a fashion, spiralling with a varying gryoradius along a non-straight field line. (They don't actually spiral along field lines, since field lines are a mathematical fiction for visualising the magnetic field).
Polarisation measurements in the spiral arms indicate that the magnetic fields there are pretty tangled rather than nicely aligned. So the direction of motion of cosmic rays becomes isotropic on essentially the same distance scale as the scale of the 'tangles', at least for cosmics rays of low enough energy to have $\approx 1$pc gyroradius. Directions will be randomised on a distance scale comparable to the scale of magnetic field fluctuations or the gyroradius, whichever is larger.
If cosmic ray sources were primarily at a distance of the order of a parsec, we'd see anisotropy because the cosmic rays simply wouldn't deflect in direction of travel that much before they reached us. But they are apparently significantly further away than that. And also typically further away than the charactersitic distance scale of magnetic field variation, or else that would also cause anisotropy.
So the short version is that it isn't the large gyroradius in the galactic magnetic field that makes cosmic rays isotropic, it is that the isotropic cosmic rays are coming from distances greater than the gyroradius (and the magnetic field length scale) so their direction of travel has become essentially randomised.