Ok, this is my take, and I have to say first that I have not done soil this way. I have done coco, and recently Sunshine #4 which is a low nute peat mix to which I have added lots of perlite. The problem with soil is that if it is not well enough drained, particularly if the pot is large relative to the plants involved, flushing may result in overwatering stress for the plants - i.e. lack of oxygen in saturated soil. I do not know enough about your soil mix to know what your specific risks are.
Having said that, when I flush, I use nute mix at the EC and nute makeup that I want to use, I do NOT use plain water. Flushing with plain water, in my opinion, subjects plants to excessive osmotic stress, although I understand that many growers do this and get away with it. I use salt based nutes for flushing, and see no realistic option for getting the job done with organics. The flushing process will remove a lot of the organic stuff that would otherwise be feeding your plants, but at this point in your grow you may have no choice.
When I flush, I top water with my nute mix and collect the runoff until at least the EC of the runoff is on target more or less the same as the input. Once I get to that point, I know that the medium is at the EC and, with coco at least, the pH target, so the job is done. Unlike my experience in coco, in my peat mix, I found that it is so strongly buffered, presumably due to the dolomite lime in the mix, that the runoff stayed at ~6.5 no in spite of the input pH (I used 6.35, then 6.2, and finally 6.0, with zero difference in runoff pH). As
@Mañ'O'Green has so often pointed out, if you are supplying nutes, they need to be a complete and balanced package. In my last flush in Sunshine #4 for example, I used Megacrop II with just a small dose of cal mag.
Anyway, if I were you, I would make a decision on your target pH and EC, mix up a lot of nute mix (I used close to 4x the volume of the pot) at your selected EC and pH target, and keep flushing until you get the runoff to the EC you choose. You may or may not get the pH all the way due to buffering, but I would not worry about that, the buffering is your friend. Once you get the runoff to where you want it, you will need to let the pot dry out well before watering again. In your setup that will mean at minimum siphoning or vacuuming out all water from the reservoir until no more drains into it, and then leaving the reservoir empty for at least a couple days before watering again.
All just my two cents of course, others may well have contrary ideas, especially growers using your SIP/organic approach. Bottom line is that if you do not do something effective, your grow is looking headed for trouble. So, although a flush comes with risks of overwatering, and may bugger your pure organic hopes, it may nonetheless be your best available option.
Good luck with your decision, please keep us posted on how you make out.