A low traffic area would be one where you an your dog aren't walking around in. Like a spare bedroom you would only need to enter to deal with the snake. If you don't have a spare room at least make sure he is in an area you will be in the least.
Him not moving in cage could mean something but it also might be nothing. Carpets can be a more active snake but at the same time they are still snakes and snakes in general don't move around a lot. Also he could be moving when you ate sleeping or not at home and just going back to the same spot.
Handling him less is probably a good idea but you might still wanna take him out once or twice a week quickly just to check him over and make sure he is ok. If there is actually something wrong you wouldn't want to miss it and have it go on to long. How much did you handle him before you started to get worried?
By the sounds of it though if he is healthy, his behaviour sounds normal. It's just different then what it used to be. Keep an eye on him though just in case.