Is the argument of perihelion random?
Argument of perihelion or most planets/bodies changes very slowly over time due to higher order perturbations from other planets' motions (mostly Jupiter and Saturn for the solar system). General relativistic effects also cause the perihelion to advance over time, though this effect is smaller than the others for most purposes.

So given enough time, the arguments of the planets' perihelia would likely end up being fairly randomly distributed at any given time. Also, the planets' orbits are often dynamic on such timescales due to the effects of higher order perturbations showing up, which can cause eccentricity changes, which also affect the positions of perihelia.

So, my guess would be that it is okay to have the arguments of perihelia randomly distributed, since it is inconceivable (at least for me) that any sort of resonances would be visible at this level in order for the distributions to be non-random.