dresali: I do not like your suggestion, because when someone offers draw and I do not want draw, a natural way to decline is just to keep playing, and your way would enforce to answer a question "do you want draw" before continuing, and this I do not like. I hope you understand my concept about "playing one move implies declining draw offer"

Well, this is a luck game, so a K against K endgame is not draw

A simple solution is to play your move, and, after your move have been completed, if the behemoth position is not to favorable for you, offer draw at that time, which seems fair, am I wrong?
Regards

PS: it is possible to offer draw even when it is not your turn to play