You can possibly combine the two games and try and gain support from both camps. Play call shot (maybe) and allow a push out after a called safety. Allow only one or two called safeties per game and the same for push outs.
You'd lessen the safety play and BIH's and still have the push out option. After two safeties, you'd have to shoot for the pocket. Allow two way shots at all times, so kicking would be involved.
If you used up your pushes, you'd have to kick or give up BIH. Safety play would force the opponent to use up their pushes or kick for the ball. Limiting the number of safeties would encourage a strategy of using two way shots to limit your opponent's access to good position if you miss a shot. Pushing out after the break for the breaker does not count as using one of their pushes.
Best,
Mike
That may be a good game, but I'd need a caddy or somebody just to keep track of all those options before I'd know what to do. I don't think adding more things to it will make it easier for the non-pool crowd to get into or watch.