[GroundUrMast]

OK, a few random thoughts...

If your chief concern is reducing risk of lightning induced damage to mast mounted electronics, a lighting rod above the equipment (including the antenna) would be worth considering.

I agree with the old-timer, that the tower ground system should be integrated into you existing electrical service grounding system. I would not use a #12 or #14 branch circuit ground lead, it's too small in diameter to deal with the current involved with a lightning hit or even near miss. Also, there are likely many sharp bends in the branch circuit cable run which will add impedance at RF frequencies common to lighting discharges. Do you want to invite lightning induced fault current to follow a path though your existing wiring?

I would use a dedicated run of wire, sized for the purpose. Though it's not prohibited by the NEC, I avoid running antenna and mast grounding conductors into or through a structure if at all possible. If there was no guidance from the tower manufacturer, I would use #6 AWG copper (minimum) based on my lay person knowledge of NEC article 810 & 250. Because the documentation for your tower calls for #2 AWG, I would be inclined to go with #2 as the minimum for the bonding conductor from the tower to the new rods as well as the bonding run back to your electrical service grounding system. If your electrical system uses multiple rods and/or connections to pipes, foundation steel, etc, the NEC or local code may dictate an upgrade of the bonding in the existing electrical service ground system. If I was installing your tower on my lot, would replace the #6 AWG that runs from my service panel to the two existing ground rods with #2 AWG. This would ensure that the path from the existing ground rods to my service panel and ultimately the PUD neutral conductor is capable of carrying the current of a ground fault (due to lighting or any other cause) from the new tower being connected to my existing electrical ground system.