My HT buddies run their wires through the ceiling. I don't know if you can do that but it is an option in some cases.
i would not run your cables under the rug. the idea is to get them off of the rug. you have so much power running through those cables from the amp the rug will interfeir with the electrical flow and the idea is to get the electricity from one end of the calbe to the other with no interruption the rug will stop this from happening and degrade your sound. what about under the house.
Thresholds can be easily removed, modified by routing space for some cable(s), and replaced; or a new threshold can be purchased, routed, etc. Any decent carpenter or many lumber yards could easily do this. Cables can be run around the perimeter of the room under the wall moulding, if it is thick enough, to keep them a bit away from the carpet. All of this likely requires very long (and expensive)cable runs, and, if the accounts of the deleterious sonic effects of modern synthetic carpeting are true, ceiling runs seem far more practical on all counts. Good luck.
Why not do it through the wall properly...with receptacles? If you are handy with a giprock saw and a screwdriver you could make a neat job of it. As long as you are dealing with signal wires (no 120 VAC) you don't need an electrician. Just my two cents - I have done this several times. It ain't cheap but it looks professional.
Is there a door at the "door threshold"? And what is the subfloor, wood or concrete? Also, what is the w-2-w carpet material, wool or synthetic? Does it have antistatic threads woven into it? These are all important with respect to deleterious effects on signal transfer. You don't have to worry about the RGB, and if you're running speaker cable that far, I assume it isn't to your main speakers? The critical one is the Maestro IC.
My solution to this issue is to cut a strip out of the carpet right under the (closed) door and install a low profile (about 1" of space underneath) aluminum 'saddle' threshold in the space (about 3-5 inches wide depending on the extrusion you choose) running the cables under the threshold. HD carries them in natural, black/bronze, and gold. Pick the best match for your carpet. You can also have them custom anodized or powdercoated to match your carpet exactly, but that starts to cost.;-)
Just don't mix low voltage and high voltage into the same raceway, where ever it ends up being.
If you have a basement just drill through the floor at the threshold, come up the other side of the Threshold and continue with Wiretracks around the room. Two holes seems to make more sense than modifying an entire threshold.
If no basement, then modify away, or.....Go up and around the Reveal of the door itself, which requires the casing be removed. Uhhgh! Not to mention longer cable runs.
My experience with my own HT install for my Pioneer Elite TV is that it is not easy, or cheap to get it done the right way. I personally refuse to own a flat panel on a stand, to me they belong hung on walls, and this take some creative thinking in some applications.