Anyone in Dallas - Professional Wiring Help, will pay $$

I'd get some names from the CEDIA website.

Using the drywalled garage below for access would be pretty easy, and it's dirt cheap to repair drywall. Might be super easy if the floor joists are parallel to the run.

There won't be enough room behind the shoe moulding. The baseboard is possible but then you're still going to have sheetrock damage pulling it out and you'd have to glue back to avoid nails (if you can salvage the original).

If you're accepting of using moulding to hide the cables, why not use this as an excuse to install some crown moulding in that room? Since you have a fireplace below you're TV, it'll be easier to route the wires up instead of down. Depending on how much time you want to invest, you could even do it on your own. The hardest part of the job would probably be cutting and installing the crown, but even for that there are plenty of short cuts nowadays.

Usually a gap behind crown molding.

Most people don't want to run new cables because it's a pita to fix drywall yourself, and paint. Since you're painting anyway, I would reschedule the painters until you have the cables installed.

DIY Drywall repair can be frustrating and time consuming, if you're not experienced. Hiring someone to do it is very easy.

You can cut holes in the drywall at the top of the walls, and hide the holes behind the crown molding. And, you could run the cables around the room behind the crown molding.

Just reschedule the painters until you have the cables sorted out, and avoid the cost of the crown molding. if you were doing crown molding yourself, there would be less of a chance to nail a cable, but that is a concern.

You can run the cables in the drywall ceiling, below the floor in the garage ceiling, or behind crown molding. You have lots of options.

And yes, behind baseboard is also pretty easy. Pull the baseboard, cut a 1-2" channel in the drywall, and the cables fit in that channel. But careful of nailing cables. If you DIY the cable installation, and have the time, you can drill holes in the center of the exposed studs behind the baseboard and channeled drywall, and install nail plates on the drilled studs; the cables pass through the studs this way, and there is less of a chance for cable damage from nails.

Make sure the cables will fit behind the crown molding profile you choose.

Run it by the trim carpenter first.

Don't staple category cables.

Test the cables ASAP, to make sure they're not damaged.

I'm not sure if you can bend a category cable 90 degrees, and have peek performance, i.e. 10Gig data speed. Supposed to be gentle bends. Will most probably be fine for gigabit, not sure of 10Gig. I have no experience with 10Gig.

In 10 years, and you attempt 10Gig, and it doesn't work, will be easy to add more cables through the garage ceiling drywall.

You can staple them in place - just use a cable tacker which has rounded staples for this exact purpose. But assuming you're just trying to get them in place so they're not hit by the carpenter - duct or masking tape!

And by "sharp corner", we mean a real 90-degrees - don't do that. But a bend radius of 1" or so isn't bad. Hold the wire in your hand and turn it back towards itself, you'll see that you get about 2" of loop width (diameter) without forcing the wire...

Jeff

What kind of crown molding trim? Some people use PVC now - not sure if that would allow you to run cables behind it. Conventional, standard wood crown molding trim usually has space.

Discuss it with the trim installer/carpenter. Just pick crown that has plenty of room.