Drill up, inside wall with least damage to wall?

I'm trying to run some coax cable from a splitter in the attic (accessible) to a room on the other side of the house. Normally one would just worm over to the top of the appropriate wall, drill a hold in that 2x4, drop the cable down and be all ready to hook it up to a wall plate.

But in my case, the top of that particular wall is not accessible - there is an impassible barrier in this very low-roofed attic. Nonetheless, if I could drill the hole from inside the wall, I could push a snake/fish up through it, and hopefully reach the accessible attic area. Then I'd pull the cable (and a backup twine) back down by retracting the snake.

First up, does this sound like the right plan at all? Second, what's the best way to drill up like that? I could cut a hole in the wall big enough to put my entire drill into, but is there a better way? I also have a Dremel, and they make a flexible exension, but I'm not sure if that could drive a large enough bit through a 2x4.

The good news is, if I do cut into the wall near the ceiling to do this, I can do that from inside a closet, so the subsequent repair doesn't need to be perfect. I could even cover it with an access plate instead of repairing it, in case I wanted to get back in there.

Thanks,
Greg

Actually Greg,
It sounds like you already have it all figured out

For drilling up into a wall plate at the ceiling, you could use a long auger bit.
Cut a slot in the wall wide enough to accept the bit and drill at a slight angle.
A good electrician can run an auger bit into a wall and angle it to cut it's own slot in the drywall.
As you said, you're inside a closet, you can get away with a little bit of experimenting there

Would a 3.5 amp Black&Decker corded drill be sufficient to power said auger bit? It doesn't need to be a big one - I just need a hole about twice the diameter of coax cable.

Also, what do you think of using a right-angle attachment on the drill if I go for straight up instead of the angled approach? I don't have a right-angle drill.