I think this idea has some merit. It might help increase entries. I would definately say let's take the "unlimited" entries off the table now. I know some State tournaments allow you bowl additional Team events, but don't know of any that allow additional D/S entries.
There are multiple ways to look at cashing....you can allow people to cash multiple times in team and doubles if you force them to change a minimum number of team members, and bowl with a different partner the 2nd time around or make them stay the same and only cash once. If you say you can only cash once....do you take their highest score, their first score, last score, etc. And what about All Events....do you take their 3 highest series, the first 3, last 3. And what about the year long side pots and Super brackets. How do handle paying for and paying out for these items? Such as 30 Clean, High Game sidepots, etc. As long as you spell the rules out specifically around this, it might work. You will always have people complaining no how you structure it though.
Taking all that, and probably other things I haven't thought of, this would be my proposal:
You can bowl a maximum of 2 team events. The 2nd team event must have at least 3 players different from your first team entry. You may cash multiple times in team event.
You can bowl a maximum of 2 Doubles events. THe 2nd doubles event must be with a different partner than the first. You may cash multiple times in doubles
You can bowl a maximum of 2 Singles events. You may only cash once in Singles. Your highest score will be your singles event score.
All Events consists of the first series you bowl in each event. For example if on Day 1 you bowl 2 team events, Day 2 you bowl 1 D/S event,and Day 3 you bowl 2nd D/S event. Your AE score will be your first team event on Day 1 and your D/S scores from Day 2. You may only cash once in All Events.
Sidepots will now be per event. So instead of paying $10 for all 3 events for the 30 clean, or 3-6-9 Strike Jackpot....it will $3 per event (thinking maybe make it $5 so more even, not sure on that). Super Side pots are already per event, so they can stay at $25.
Super Brackets are a tough one. You can't allow people to enter twice or potentially they could wind up bowling against themselves somewhere down the line. I have two options on this one and I am torn. You can handle like AE, using your first series in each event and keep the cost at $25. Or you can use this as a way to generate interest in multiple entries....raise the price to $30 or $35 and let people use their highest series in each event.