When you say 'throws the chain off the ring' do you mean it just drops the chain to a higher gear or throws it completely off freewheel and onto the hub? Could it just be a low limit adjustment problem on the RD? When you're set on big/big how do the pulley wheels line up in relation to the sprocket? They should be just slightly inboard of being centered and if they're any further you can use the low limit adjusting screw to return them to the proper alignment.