Methods requiring patching is sometimes the only practical option. A small hole in the wall surface below the top plate will permit drilling up through the plate from below. The drilled hole can be at an angle, keeping the drill motor outside the wall.
For a compact angle drill for tight places, this is the smallest I have found. Shopping might find a better price.

Here is a link that might be useful: Drill

A long dill bit (24 inches) at an angle will make an elliptcal hole inthe drywall, and then o through the top plate.

Feed a fish tape up into the attic, and then snag the end with another fish tape and pull the lower fish as far as needed into the attic.

Attach the coax to the lower tape and pull it though.

You can then detach it from the fish (make sure there is enough pulled through to reach the desired location in the stud bay) and shove it into the wall.

Cut the hole for the faceplate and reach in an grab the coax.

One nice thing about low voltage is that you have many more creative options for hiding cables.

While I understand you don't want run along the baseboard, can you can dado out the backside of the baseboard for the cable? Coax also tucks very nicely between the carpet tack-strip and wall.

Any possibility to run between the second story floor joists room-to-room?

Then again, what is signal you are distributing? Are there any wireless options?

Also, while I detest under-carpet cables, CAT5e can lay pretty flat and never be noticed.

Unfortunately the rooms in question have hardwood flooring. Pulling the baseboard might be an option, although now I wish I still had my router table...

The coax is for cable TV. Comcast doesn't seem to offer a wireless option, yet.

Joists go the wrong way for a between the floors option.

As for drilling to top plate, the roof has a pretty low pitch and while drilling at an angle seems like an option I'm wondering about the geometry. I haven't looked but I'm assuming it's a double top plate. At 45 degrees I'm going out 1" for every inch down. Or do I drill into the side lower plate?

Of course, laying on my belly with my face in fiberglass insulation and the back of my head just inches from nails through the roof deck while drilling accurately sounds like so much fun....

"Of course, laying on my belly with my face in fiberglass insulation and the back of my head just inches from nails through the roof deck while drilling accurately sounds like so much fun...."

That is what fish tape is for.

You feed up a piece from below wit a hook in the end, then hook it with another piece (or even a fiberglass pole also used for dealing with wiring in hard to access locations).
You may need a propane torch to soften the steel of the fish tape so it can be bent without breaking to make a hook (fish taoe is normally spring hard steel).

Be careful what you try and cut it with.

It is hard enough to damage most 'wire cutters.'

A cut of wheel in a Dremel tool works well, or you can soften the steel with a torch first.

Sometimes you can bend it sharply enough to break it off with two pairs of pliers.

Since your situation offers no perfect solutions that are also easy, consider a cable outlet on one of the (at least) two walls that are at right angles to the outside wall which has the eaves. A couple of feet in from the eave wall, the roof clearance is greater for working from the attic. Would an outlet in one of those walls be helpful? If more patching is acceptable, the cable can be run horizontally in the wall by cutting holes about the size of receptacle boxes on each side of each wall stud for drilling the stud and pulling the cable. Whatever you want can be done. Deciding how much work or money one wants to expend is really the question.

Again, since this is low voltage wiring, another option to keep in mind is to cut a groove/channel into the outer surface of the drywall and then run your cable in it. Afterwards - tape-mud-texture-and paint.

While usually used as a get-around for headers over a sliding doors (ie with cathedral ceilings) and such, it may be something to keep in mind.