Flow Balancing Valves - control strategy

Hi all, i'm after some help on a flow control valve control strategy. There are 8 parallel vessels that require evenly distributed flow.
Each vessel features a flow control valve on the inlet, and a flow transmitter on the outlet.

Currently the algorithm is:
1. Add all flow values and divide by number of vessels = required vessel_flow.
2. Individual Vessel flow - required_flow = DiffFlow
3. Each control valve has a PID controller that will modulate the valve position to set DiffFlow to zero.

This works well and will balance diff flow within 0.1L/.s. (Total flow upto 180 L/s).
This issue occurs after the the most restrictive vessel changes, all valves will readjust and bring diff_flow back within spec. However, now none of the valves are at their maximum value, introducing further resistance on the system.

I need a way to bias the balancing valves so they are all trying to open further (while none are at maximum value), while also maintaining balanced a flow.
I'm thinking a periodic addition to all valves, or a cascaded loop that will try to increase "average valve position" etc

Any ideas, comments or thoughts would be awesome!
Why not bias the Differential flow value (individual vessel flow minus (average) flow) because that's the PID controller's setpoint, right? Use the same bias on all controllers simultaneously.
If you need more ideas then describe the process more before the flow control valves, ideally P&ID sketch. What supplies the fluid to the control valves, pump? gravity?