My understanding of the Liquidator was that the flow rate was determined more by the suction side than the pressure side which is why they suggest putting the flow meter on the suction side. They use float shut off valves on the pressure side so that it will only fill to a certain level and then shut off. The suction side works in a similar way but will shut off if the level gets too low. Since this is not a pressurized system, the suction side and pressure side are pretty much independent although not completely. Also, since the pressure side has much higher positive pressure than the negative pressure on the suction side, the suction side is usually the limiting factor for flow rates.
So here is what I think may be happening. When a solar system is engaged, two things will happen. The pressure on the return side will rise and the vacuum on the suction side will decrease. Since the liquidator draw rates are determined primarily on the suction side by the pump suction and the valve setting, when the solar is engaged, the chlorine/acid flow rate should decrease. However, since you have the flow rate meter on the pressure side and the pressure is much higher with the solar on, then initially the flow rate meter may make it look like the flow rate has gone up. After the liquidator reaches the max fill level, then the fill valve will start to close and the flow rate should be closer to what the suction side is but it may oscillate some so I am not sure you can really trust the flow rate meter if it is on the pressure side.
So getting the flow rate to be the same with solar on and off may not be very easy to do. I have the same issue with the DIY acid dispensing system I have shown
here. By the way, this system works on nearly the same principle as the liquidator except for the dilution on the pressure side.
You could try and reduce the pressure side flow rate so the tank level drops and then the suction side flow rate will reduce some because the float will reduce the flow rates but I think that would be difficult to get right and consistent. As the filter gets dirty, then all of the hydraulics will change and flow rates will change again.
Instead of a pressure regulator, you really need a vacuum regulator. Unfortunately, these are hard to come by with small vacuum levels and chemically resistant to chlorine and acid. I have yet to find one that would work well.
So I think the only solution may be to work with what you have and set the flow rates for the worst case conditon (i.e. solar on) and for the minimum chlorine level needed based on the CYA/chlorine chart. With solar off, the chlorine flow rate will be higher and your residual should climb some but it shouldn't be that much higher and little more chlorine shouldn't be an issue. And if you run with solar on most of the time, then it should have little overall impact.
[EDIT] - Just saw the additional posts while I was writting this so I think we are all on the same page.