What you just described is a sh*tty course in my mind. Not enough staff, one guy working the pro shop? How about the starter and the rangers? And I completely disagree that people don't listen. It is proven in every organization and industry that people will adapt and follow guidance and rules when properly indoctrinated and educated. Do you think golf just became a gentleman's sport by chance? No, new golfers followed the precedence set by those they watched and played next to.
I'm not saying the idea is terrible, I just think we look at it differently. You want to build a system that works with no influence from management, and I think management is the only way to accomplish the goal. You're using money to keep the course short and reward fast play (although it only works if everyone is looking for the bonus.)
I don't want to come off like a rich *ss, because I'm not. And maybe it's geographic in nature. But saving $5 or even $10 on a round isn't going to make me shorten the course or speed up play. Courses I play (about 10 in the area) cost $65-100 per round. Add cost of drinks, food, tips for cart girl, tips for kid that wipes down my clubs, etc, etc, and it's a $120+ day pretty much every time.
What does work is knowing a course is well managed and well staffed. I've witnessed it and it works. Pro shop welcomes you to the course and while checking you in, talks about pace of play and course rules. Starter then takes 5 minutes to reaffirm what ready golf is, makes recommendations on proper tee box, even shows you how to properly repair a divot and gives you a cheap little plastic tool if you don't have one. 1-2 rangers actively roaming the course, asking you to speed up if necessary. When a group of guys witness this, they think to themselves, "wow, nice course, they are focused on making this a nice day for us."
And concerning gps, there is no fiddling. Other than pushing a button to order lunch at the turn, you don't touch the thing. It's active, gives you distances at real time, and again reminds you if you are ahead or behind. With all the discussions concerning gps and range finders, the one commonality is that they speed play by eliminating the pacing off of sprinkler heads. I'm sure you've played with a fore caddy before- talk about a fast round. Why? Someone is there always educating you about the hole, giving you distances, etc.
Again, just difference in opinion. I will also gravitate towards a course that is well run, because I know my chances of having an enjoyable day is better.