You are the first to address the problem directly. I have had problems with this for years.
1. yes you have to optimize the first parameter for each time window.
2. then you set the first parameter fixed for each time window. And optimize the 2 for all time windows.
Time window: 1,2,3
1st parameter: 34,12,22
2nd parameter 9,3,9
3. then you also set the fixed parameter for all time windows and make the 3 parameter.