I have a bit of experience with this from my short amount of time spent doing telephone installation and Repair. If we found a home without proper(or non-accessible)Earth grounding, Then we would install a ground rod for them, free of charge, as part of the protector install. No one enjoys lightning strikes in their ear.
You could get complex but the simple answer is that reconnecting to your existing ground rod should be fine. Just be sure to use (at a minimum) whatever is code for your area for the guage of wire. We used 6 gauge. I think 8 might have been the min. Ground wire (in Canada anyway)should have a green sheathing to help identify it as such. Your code may require that or similar.
A good splice would be fine electrically (for a while) but I would strongly suggest that you run a new wire the whole way. If you do not have access to grease filled splice enclosures (or want the ugliness of one hanging off the wire outside your house) than it makes more sense to run a new wire as splice points are a common point of corrosion that can reduce the conductivity at that point.
Pounding in a new rod should be fine too. However, I'd suggest digging a hole to depth first. Then refill it with rock free earth and the rod. Pack the earth down tightly every foot or so as you fill it. Trying to pound it down through rock filled earth is not only hatefully hard to do sometimes but this can also damage the rod.
Grounding can be a lot more complex than that, but you are just trying to replicate what the electricians did before, so you should be fine.
I know nothing about the fancy ground rods you mention. I suspect things have changed since I did this work. Are these made by Monster by chance? snicker....
