First of all, "taking care" of heavy tippers and board members is a human reaction. It happens in restaurants, hotels etc. I am not saying that it is acceptable, only that it is a human thing and is done all over. What is not acceptable is ignoring those that don't tip. If a resident is entitled to a service, then the super is compelled to provide that service as that is what he/she is paid to do.

Secondly doing private work on company time is theft of service. This is also not acceptable and should not be tolerated. Theft of service and ignoring those that don't tip only show the true character and integrity of a person (super or otherwise). So perhaps the real issue is you need a super while being human has the "right stuff."
To echo ADC, board needs to put policies in place to make sure that private work is to be allowed or not and place guidelines if it is. Without guidelines then you have a Dodge City.

Third the private job "chargeback system" creates a lot of paper work both for super and management. In some cases it works in many it is more of a pain then its worth. Some management companies may increase there management fee to provide this, as it is a lot of book keeping. Furthermore, most workers need to make extra money, and there is nothing wrong with it as long as honesty and integrity is observed. The private job thing is a way to make extra money and also a way for the owner to save money as well. When done right, it is a win win situation.

Forth and last issue, I have yet to see a work order form that has a section for satisfaction. In my buildings, every year or two I send out a survey of satisfaction form to be filled out by residents grading various performances of staff etc. This might work for your building as well.
Pgrech