The photos help immensely. Thank you.
Nice house... beautiful antenna
I own a 3/8" 'telephone' bit. It's about 24" long and is able to make it through several layers of framing, sheeting and siding when the need arises. I believe you can find such tools at Home Depot, Lowe's and similar stores. If not in the tool department, then the electrical department.
If you run the coax through the attic gable ends then down the west wall to meet the existing coax, run a #10 copper wire also. Connect the #10 wire to the mast/tripod and then to the electrical service ground. I assume there is a splitter on the outside at the west end. If so, verify it is connected to the electrical service ground with a piece of #10 copper wire.
(The #10 wire can be insulated or bare, what ever looks good or costs less, your choice.)
Your other option looks like running under the soffit which will add a bit to the length of the coax run.