Have you tried Milliput to make the caps stay on ?
It's a two-part epoxy putty, very sticky when freshly mixed (use water on your fingers and tools to stop it sticking more to them than the mushrooms....). You could make a ball or disk of it, push the two bits of shroom together, then use the wetted back end of a paint brush to shape it more if you need to.
That is a good idea, thank you. Now I watched some videos too with tips on how to use Milliput.
At the moment these mushroom caps just found the balance and with the temporary stems. Once again, thank you for the suggestion, I am sure it will come in handy for some next mini project ;)