If this were mine, I would add another ground rod about 20 feet from each end, And then one more in the middle. A total of three more rods. Total of 5 rods for the entire run.
What engineering basis do you have for recommending more rods? As you point out "installing them too close... is poor economy", and I think the same would apply to number as well as spacing.
Not that more rods isn't better (it is, in general), but where is the cost/benefit tradeoff?
Let's look at the physics. There's three reasons to connect to the soil:
1) RF ground for an antenna where the soil is part of the radiating system
2) Electrical safety, in case a power line or other live conductor comes in contact with the antenna
3) Lightning energy dissipation
Ground rods in the middle of the bonding run do nothing for #1, because the AC resistance of the wire connecting them is sufficiently high at amateur HF frequencies that it's like hooking a big resistor between the "ground" and the antenna.
Ground rods in the middle of the bonding run do nothing for #2, because the DC/60Hz resistance of AWG6 (<0.5 ohms in 100 ft) is so low that the voltage drop along the wire is small in the event of a fault, so that all the equipment stays close to "bare feet" potential. (one of the reasons for NEC grounding)
Ground rods in the middle of a bonding run don't do much for #3, because the inductance of the 20 feet of wire to that middle rod is about 6-7 microhenries. At the nominal 1 MHz for lightning, that's an impedance of 18 ohms, and at, say, 1 kA, that's a voltage drop of 18 kV. Buzzing along to the next rod, the current is less, but the inductance is more... The net result is that the added rods don't add much to the effectiveness of a lightning ground. If you're worried about reducing the impedance of your lightning ground, drive more rods near the antenna, or even better, bury some radials, or, if the antenna has a concrete base, make sure it's well connected to the grounding system.
Take home message:
The bonding rules aren't for lightning or RF. They're for line frequency faults and shock hazard. From that standpoint, it turns out that the bonding really doesn't need to be connected to "earth ground" very well at all. (and in fact, the NEC code makers are gradually changing the wording from grounding to bonding)
Long wires (unless buried) make terrible additions to RF grounding system.
Lightning is all about keeping the strike energy somewhere other than delicate stuff, and making sure that all equipment goes up and down together. The currents are so high and the rise time so fast that trying to keep the voltage "low" is impossible.
Ground rods worked great for Ben Franklin, because they replaced *nothing*. But there's a lot of better ways to do it now, and we know a LOT more about the underlying physics and applications.