I like the way your mind works. Anything to cut down waste is a win in my book. Unfortunately, the wasted plastic negates the recycling effort.

Do you have a woodstove, fireplace or outside firepit? If so, you can do the same thing to create paper fire logs, as well. The wet paper compresses quite well and even magazines can be used for that. They are so dense, they rival actual wood logs in burn time.

As for an idea to save the cup, you can spray the cup with oil before packing in the paper and hopefully it will just slide out.

The next step will be to find a more feasible way to mold the paper cups. Since they do not need to be perfect, I suggest trying to make them thicker and just shape them by hand and see if they hold their shape until dry. Then you don't need to have a mold and a process is skipped, making the task more efficient.

I look forward to seeing what you come up with. Great job!