Solution for the lag will be a special category "bot play". The bot will not be programed but will behave like a black box, computer ai will record you every time you play in a local game and will slowly build the bot around. Then the bots will compete on a server, maybe separated by categories determined by previous recording time.
I worked at NASA (AMES) on a project to put small mobile robots on the moon. Our biggest goal was to create a tele-operated mode where from earth we could actively roam around the moon. The hardest part was that factoring in a 4 second delay from our commands to the network stacks to the rover on the moon, and then that video from the moon back to our computers and then creating good judgement. A 4 second delay seems insignificant but is in fact detrimental to intuitive controlling.