Hi! Thank you for checking the game !
The only way to speed up time right now is to kill your character by triggering the spikes or axes as we didn't have time to make a proper end button but we plan to add one in a future version.
Also the stone can't push buttons wich isn't really clear I do agree because the idea was to have different gorgons applying different property to the block and the base ones don't have gravity /can't push buttons.
As such you need to put a box on them to make the button press persist throught the last character right now.
Sorry for the lack of indication but I hope you still liked your experience ^^.