Running along side each other is fine.
But my preference is to keep the mast ground outside the structure even if it makes more work. The same is true for the coax, I prefer to keep it out of the structure until it has passed through the grounding block.
An isolated ground rod offers very little protection and in some cases, can set you up for a significant voltage difference between objects that you think are at ground potential. If you add a ground rod, you should bond it to the existing ground system with #6 copper. In your case, it sounds like a run all the way around the house.
I have a detached garage with a mast. I spent the money and time adding a ground rod at the garage, 30' to 40' from the existing electrical service. There is a permanently install #6 wire connected to the new rod at the garage and the original rod at the electrical service at the house. So far, I've made it though a couple of nearby lighting strikes. The last one, a few months ago fried a neighbors gate opener controller.
http://forum.tvfool.com/showthread.php?t=901