You've asked a great question and as other posters have shared, getting a copy of the ARRL grounding manual is a great idea. I'd also suggest a PDF "Motorola R56 Standards and Guidelines for Communication Sites" about grounding towers and radios.
The initial problem that I see in your description is your use of two separate grounds - one for the antenna and one for the electrical wiring. Your radios are wired between these two grounds...and these two grounds are not at the same potential (if using the term "potential" is foreign to you, then that is an indication that you likely need to do more research and/or hire an electrician). This difference in potential is the reason the two ground rods need to be bonded together.
With your radios located between these two differences in potential, when a voltage fluctuation occurs (e.g., lightening flash in the area), the difference in the potential (i.e., voltage) between the ground rod for your antenna and the ground rod for your electrical wiring can be rather large, and this difference in potential (i.e., voltage) is looking for some way to equalize. With your radio between these two extremes, the circuitry inside your radio will act as a conductor to equalize the difference between these two voltages. Unfortunately, the internal circuitry of a radio tends to act more like a fuse than a conductor during these events, and your radio acting like a fuse will tend to "blow" causing expensive, if not irreparable, damage.
Large electrical events like lightening are strange things...many of us tend to view voltage as DC, yet lightening tends to be AC at a variety of frequencies.
I'm sure that someone on the forum will read my posting and point out the inaccuracies with it - that's okay. I'm not an expert, but rather an amateur, and this is my simplistic understanding of the OP's dilemma and one of the potential problems he might face. Regardless of the specific physics occurring with grounding and bonding, the jest is this...please do your due diligence of research on this topic, follow the recommendations of reputable publications and/or hire a licensed expert (i.e., electrician) for guidance ...and then pray that you never experience a nearby (or direct) lightening strike :-)
-acm