How can I ensure steady flow to all the valves?

One basic way is to adjust the valves, the dry ones fully open and the ones bleeding all the pressure just slightly open, or even restricted permanently by a smaller size bushing just before the valve.

In conjunction with that, you can install a water tank between the pump and your network with an adequate head and a hydraulic actuator to stop the tank's drain till it's full.

Finally, you may need to change your pump to one with more GPM. You want to start from the easiest choice and move on to the next.

The most precise way to control flow is with valves/flow regulator. The main problem is the cost. Although, its a very basic component and its not too costly if you have too many outlets the cost will pile up.

Even if you had matching orifices, you might have issues with the pressure drop inside the pipes and corners.

Another way to control the flow would be to restrict the flow (e.g. reduce the size of the orifices). That way if you have sufficient flow, you will have a pressure increase in the network and the pressure will be the key factor diving the flow. In that case though, you'd best change the topology of your network into something like

The topology presented above will have similar running lengths to all orifices, and the same number of turns. However as you may already understand this is not optimal, since a) what you save in flow regulators you will probably be less on the losses you incur from the added lengths and t junctions and the added installation costs (more labor costs for cutting and joining) and also b) from the added lengths and T junctions the network will suffer greater pressure drops and also there will be more points with potential leaks.