Well, lets back up, and look at this as we would any other service. I can't really argue code, and code may very well allow for multiple answers...so just bear with me as I "think out loud."
The 600 amp panels are your actual "service" location, so the ground rod should be there. There ought to be a suitably sized ground wire run from there, out to the pedestals. Multiple pedestals can "share" the same ground wire, I would think.
Now for wire sizing, and over-current protection. 100 Amp breakers? Aluminum wire? 1/0 is the minimum size allowed by table 300-16- and that table doesn't allow for voltage drop over the length of the run.
Jumpers between pedestals? Sounds like you've got some problems, some 'broken bones' with 'band aids' on them.
Now, two factors affect voltage drop; the distance, and the load. I'd first take amp readings at the panel, and see just how many amps are being drawn. If the 1/0 is drawing only 70 amps, well, your problem lies elsewhere. If it's drawing 110 amps, well, you need "more power." (Bigger wire, more circuits, etc).
Then there is the matter of voltage itself. With all power "off," how many volts is the PoCo giving you? A big difference between the 'load' and 'no-load' voltages suggests that maybe the PoCo needs to make some changes on their side of the meter.
Pedestals expensive? Sure- but nothing lasts forever. You might start planning to completely re-do your park, one section at a time. Besides replacing the pedestals, you might want to replace the buried wire and change your distribution pattern.
It's not unknown for a 30 space park, over the years, become a 100 space park. This, as well as the trend of us using far more power than we did in the past, will eventually exceed the capacity of the system.