Just out of curiosity why have you decided to litter train? I'm not very familiar with the method so I probably can't be of much help in that way. What I can say is shoving your dogs nose in his accidents will probably make him more likely to go to the bathroom in that spot. A dog will go to the bathroom where he smells pee. When he goes to the bathroom on the floor it has to be cleaned with a cleaner that will eliminate the smell not only to your nose but to the nose of your dog. I believe a good cleaner is called natures miracle but other people should know more about cleaners. The time out won't work either because he will not associate the action of peeing with the time out. Dogs live in the moment and respond only to immediate consequences (good and bad). That is why they must be praised as soon as they go to the bathroom in the right place. you said your dog uses the litter box when you are not home, leading me to believe he has free run of the house when you are not there. He is not completely litter trained so he should never have free run when you or someone else is not home and watching him. you should look into crate training. The dog is in the crate whenever he can't be supervised. When he comes out of the crate you should bring him to the litter box, he should go there about 10 minutes after a meal and also at regular intervals depending on your dogs age. By crating your dog you will be preventing any accidents. Your pup will still need lots of exercise and time to play with you, but can only be out of the crate when you can watch him. Even if you must go to the bathroom you can put him in the crate until you come out. Every single time your pup goes to the bathroom in the litter box he needs lots of praise and a treat so that no good behavior is left unnoticed. While you are watching your dog if he starts to look like he is about to go to the bathroom, immediately pick him up and bring him to the litter box, if he goes in it make sure he gets the treat within 2 seconds of finishing. If your pup has an accident (which should not happen if you are watching him) do not punish him, simply put him in the litter box and see if he goes there, if he does then praise and give a treat, if not then oh well, just clean up the mess and don't let it happen again. The dog needs to learn going outside the box gets him nothing and going in the box makes GREAT things happen.
Also make sure the litter is always clean since he goes outside of it when you are home it is possible by that time of the day the litter has been soiled and the dog will not go in soiled litter.
I always prefer bringing the dog outside to go to the bathroom because there is a clear difference between inside and outside. With a litter box or puppy pads it's well you can go in that corner of the living room but not that corner, or a few inches away from that corner, and if you ever move the litter box I can almost guarantee the pup will continue to go where the litter box was before. If there is some reason you must keep him in then I understand, but you must understand that means it will probably take longer to house break your dog. I wish You luck! hope others can help more, maybe someone with litter box training experience.