That should be possible. Each slider is connected to a field or one or two variables. Both fields and variables have triggers that fire when the selection of the field or the value of the variables change. You can assign actions to those triggers to change selections in other fields or other variables. That way you can change the settings of the other sliders. You can find the triggers on the Triggers tab of the Document Properties window.
I admit that I do not entirely understand your calculation logic. Nevertheless, it seems that a word of caution is due.
If the four quarter-sliders all just display an adjusted value based on the setting of the first slider (oneway only), then you may not need an interactive slider for the quarter indicators. A value text box will do. If you want them to keep some movement space, then you can set min/max limits based on the current value of the first slider.
Because you probably want them to work in both directions, like when changing the first quarter slider, the year slider will be adjusted as well, you may end up in a deadlock situation: each slider depends on the value of the other one, whoch depends on the value of the first one etc. Deadlock meaning that all sliders may refuse to move.
You can however assign expressions to the min/max values and let those depend on the current value of the first slider and vice-versa. That way, each slider still has some room for movement (although limited).
