For a bit of claification, marking and potty training are two different thing - behaviorally speaking.
our dog feels his is the alpha male or boss of your household, and his marking anything new means he is claiming that thing.
To stop your dog from marking is going to take a bit of work.
First while your dog is in the house, he needs to be under control. This means to either leash him to you while you are going about your business or blocking him from the area where the carpet is. Given the opportunity, your dog WILL mark the carpet and anything new in his domain, including people.
So, you need to change his idea of where he is in the heirarchy of your household. To do this you need to change his potty habits since they are directly related to the problem you are experiencing.
First you need to stop letting your dog tell you when he needs to go, and stop just letting him outside to do his business.
He needs structure, going on on a leash with a choke collar everyday 3 times a day at the same time for at least 20 minutes a walk. The walk needs to have him not sniffing at every and marking at every blade of grass. When I take a dog like this out, I give him 3 to 5 minutes before I start the walk to sniff, pee and poo, then we walk. The dog walks at my side and we walk at a pretty good clip. The dog gets to pee when I pick the place, not the dog. Just before Im finished with the walk, the dog has another opportunity to do his business. When the dog is in the act of going, he gets a command to do whichever business I need him to do and gets rewarded for doing it by my praising him. I make a big deal about it. Like if the dog found a bag with 100 dollars bills filling it. This way my dog can pee or poo on command and knows that is what we are there for. There is nothing mean about this, it is absolutely the correct thing to do in order to get a handle on your dogs behavior. Let me tell you up front your dog WILL RESIST this training and may throw a tantrum or two each time you take him out.
It is common to expect your dog to put the brakes on and not want to walk at all. or to try and pull you to where he wants to go etc.
Until you get a handle on his behavior you can use a number of tricks to help keep your dogs marking under more control. You can use a spray dog repellant on or near the carpet - Spray a towel then put the towel down near the carpet on another dry towel, you can use one of those office floor mats which go under an office chair to protect the floor, only place it with the plastic nubs normall stuck in the carpet facing upwards which will make walking on it unpleasant for your dog. The very last thing I recommend is a belly band, which I do NOT recommend for long time or permanent use.
Good luck

Thanks so much Mazer! There's a lot to consider in your post.