cateng,
The diaphragm valve would be OK for shutoff, and for fine throttling if the diaphragm was mechanically moved. You are probably right that the diaphragm opens differently each time, since the oxygen line pressures can be different causing different diaphragm positions for flow (balance of air pressure and line pressure on diaphragm). I also think the friction in the sliding gate is causing hysteresis that contributes to the lack of repeatability in your system.
A pressure regulator supplies air to a diaphragm actuator, not a diaphragm valve, in typical control valve. If the accuracy and repeatibilty needs to be improved, then a positioner that compares the sliding gate valve stem position to the input (air) signal and compensates output to the actuator would accomplish more accurate control. If the gate actuator were a piston actuator, then there is additional source of friction. One brand of positioner is PMV, and control valve vendors have many types of positioners with air or electronic input signal and outputs to pneumatic, hydraulic, or electric actuator.
The sliding gate valve is not the best pattern for throttling. The gate wedge or knife blade usually has some loose fit that allows vibration and turbulent flow from partially open gate. Most small to medium size throttling applications are done with globe pattern valves. Larger sizes greater than NPS 8" to 12" use butterfly pattern valves for throttling. There are some specialized tthrottling applications that use V-pattern ball, plug, or knife gate valves for throttling. Is there a special reason for using a sliding gate valve in your flow control case?