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Honestly, a foot and a half is pretty decent working space, as miserable wiring goes. Nice dry attic .vs. grotty wet crawlspace, too. Lay out some boards if I need a floor that's not there, crawl over there and be done with it - would be my approach in that case.

The general idea of drilling a hole and running a flexible rod through it works, so long as the hole will clear both the cable/rod, and the means used (generally electrical tape) to connect the cable to the rod (making the rod/cable fatter than they are "plain"). You want a good long section of tape run the long way, not a little ring at the end. If there is a connector on the cable, it's several times more difficult and you need a bigger hole. Either use two people or very short pulls (and trips to the other end to check) to be sure that the cable is not getting kinked as you pull it when you can't see the other end of the pull. If you get hanging/hinged splinters at the end of the hole, they can impede pulling in the direction opposite the direction you drilled, so use a sharp drill bit and not too much pressure. The point where the junction of rod to cable is entering the hole is the tricky part, and finesse will win over brute force 11 times out of 12.

Grounding the mast is a very good idea if it is metal. You can get ground clamps that are designed for use with water pipes and conduit of practically any diameter. They are two curved pieces of metal that have machine screws on either side to clamp to the pipe. There is also a screw terminal for your ground wire. I would put a separate ground rod in, but bond it with your other grounds at one place.

I would recommend not running the coax over the gutter, or for that matter over any exposed roofing material period, as the cable will be exposed to UV radiation and break down faster, as well as trapping leaves and other foreign matter. I would run the coax cable around under the eaves around the house.

One final thing to mention, is to use outdoor rated cable and connectors as corrosion can be a real issue. Also check your local codes and HOA's to see if they have any restrictions to tall masts mounted on your house.