After trying to put several things in the slot without much luck, I finally thought to try a piece of pencil eraser. Looks like it is going to work! It's pretty snug in the slot, but I also added a piece of tape for good measure.
I have some blocks that need to be pressed, so I think I will use this little dude for it and see if the eraser fixed the issue! Not that I am EVER excited about ironing, but I am a little bit now, just to see if this works. I know the excitement will fade - quickly! hahaha