The biggest thing you can do to improve reserve is to allow reserve pilots to pick up open time. This will allow you to greatly improve QOL.
You could have a rule that simply says, for any trip in open time, 24 hrs before the report time any reserve pilot can pick it up.
This would reduce the workload on schedulers so it is a win/win.
Reserve pilots could then have some control on their life. If you are a commuter you could grab a trip that helps your commute instead of losing a day becuase the give you a late trip on your last day or early one on first
The company has to assign the open trips anyway so why not allow pilots to pick them up.they would probably find there are much few open trips each day.