Very cool! Is there a particular reason for the asymmetrical board (not a 13x13 square)? Would love to try playing on a Go set I have that size. Would you make the starting rows one space apart or three (moving everyone back one)?

Also, a bit of rule clarification: stones are capable of pushing any piece one space backward? Rivers, stones, allied or not? Always, except for when the stone itself was river-pushed? Likewise, river pieces can be river-moved by other rivers?

Hey there! Glad you are finding Stones and Rivers cool!
T
o answer your questions

The main reason for the Asymmetrical board is for each player to feel like they had "their" side (which worked well in playtests) but I see no reason why you couldn't use a Go Board as a wood board at home!
Stones are able to push any piece 1 space into an open space. If a stone is moving up it can push up, if it is moving down it can push down, same for left and right. 
Rivers can be moved by other rivers as well but there is only one push a turn.

Hope this helps!