Properly installing a grounded subpanel for lightning protection
This gets rather complicated rather fast, because the requirements of the electrical code partially contradict the practical requirements of radio.  Worse, finding someone able to do it properly (or approve it) requires someone experienced in both fields at once - such people are few and far between.  Fortunately there's a way to do an end-run around the entire problem.  

Use a separately derived service

Since you're already bought into installing a subpanel, you are most of the way there.  

Install a supply transformer which has the side-effect of fully isolating the supply from your panel.  This causes the new panel to become a main panel rather than a sub-panel.  You will need to upgrade the antenna's grounding system to fully satisfy the Electrical code for mains power installations.  Since it is a main panel, neutral must be bonded to ground here.  You have accomplished what you want.  

This arrangement greatly simplifies things.  Electrical people will understand what this is - separately derived service is unusual, but not that unusual - and a bit simpler than the complex isolated-ground rules.  A future electrician working on this system is not likely to botch it up. 

The transformer

This is isolated from your house's regular power system.  This is accomplished by using a transformer whose primary is isolated from its secondary, which is most ordinary transformers. 

Common sizes of transformer are 1.5 KVA and 5 KVA (a VA is similar to a watt, so 1.5KW or 5 KW - 12.5 amps or 41 amps at 120V.)   

Most readily available transformers are configurable for 240V or 480V on the primary, and 120V, 240V or 120/240V on the secondary.  You would supply it with 240V from your main panel. 

You can also obtain isolation transformers of various sizes, which may be 120V on each side. 

The main issue is whether the voltage surge of the lightning strike break down the insulation in the isolation transformer.  In this case, there could be unpredictable results.  There's no requirement to connect the grounding systems to each other, but a heavy ground connection would help to reduce this voltage difference.  Realistically you cannot put enough copper ground wire down to carry the ampacity of a lightning strike.