Little Miss
Snake poop also has urates with it and some clear liquid so not all of it gets soaked up by the aspen you are putting on top of your repti carpet. As well snakes love to burrow, so unless you can guarantee your snake has never and will never slither through its excrement or do it's business when tunneling, then hot gluing down the repti carpet is a very bad idea. As well snakes tend to get in and out of their water dishes therefor spilling water.
All of these things allow for the growth of mold and bacteria in your repti carpet. Even more so because you have covered it with aspen, as you prevent it from drying out quickly and you keep it covered(dark)... just what mold and bacteria love to grow. Some molds and bacterias like warmth and some like cool, your snakes tank will provide both.
By only washing the carpet when you clean out the tank, you are not ensuring it is completely dry and cleaner free when you put your snake back into the tank. It cleaner residue is in the carpet you also risk poisoning your snake.
When ever repti carpet is used it should be thoroughly washed, rinsed and dried regularly to prevent, disease, bacteria, mold and parasite growth. That is why it is suggested to those who use it to have two pieces cut thatfit the tank, so that when one is dirty and being cleaned, rinsed and dried the other one can be put in.
If you are concerned about your snake getting under the carpet a better solution would be to use aquarium silicone and silicone Velcro around the bottom edge and then sew the other Velcro side onto the edges of the carpet. Thus you have a removable carpet, that can be properly cleaned.
Just some things to consider...I would hate for your snake to get sick and you to have your good intentions back fire.