So a few questions on all of the above, and I did see your post on the main GF thread, but first to be clear on what you're trying to determine. I presume you wish to get to a well controlled mash temp in the grain bed, which is where I, but not all folks, believe the main action is occurring. That being the case, then it is truly reasonable to believe that the GF temp probe is relatively meaningless, other than it is what will turn on/off the heat. So, focus on bed probe only.
Now, ime, I have had a consistent recirc whereby I begin with the valve in ~30-40% open for first part of mash, rising to ~70-90% open after 15 min or so, all done to 100% eliminate any overflow, I wish for all to run through the grain bed- another point of contention where plenty of others have no issue w/overflow. I also hit my grain at dough in w/ ~+10F water temp. After dough in I find I'm at strike temp almost perfectly (I measure the bed temp prior to putting on top plate), while the GF controller will read about +10F! Thus, I ignore. This settles in about 10 min or so, and the heat will come on maybe twice during the mash until its done or I ramp for a mash out.
So, what I'm trying to say above, is that your experience is not surprising. I think wide open valve will have 60-70% of the water recirc without ever going through the bed at least in the beginning using my estimated experience as a guide.
Finally a few things to also consider. One, all temp probes have been calibrated to same measuring points (GF for me was right on with my temp stick). Two, you perform the mash with setting on mash. Three, you strike at a higher temp, will drastically reduce your initial variability as the recirc wort doesn't need to heat up the grain bed so much.
In all of the above, I'm not so sure how much difference to your final beer all this makes. I've read the brulosophy exbeeriments on mash temps and found it interesting, even without scientific replications completed, its still one of the only sources I've read on this, and interesting results.
Good luck!