Good news!
It seems that I got my GPS working again. Apparently the upgrade was not the root cause for it to start working, only a side effect of the upgrade (that it cleared all traces of AGPS data cached in the system) that made it function robustly.
It seems that under some conditions (maybe on this chipset/software/apps whatever combintation) the AGPS reset doesn't actually reset the GPS data (neither from GPS Status and toolbox, not GPS test) even with Airplane mode on. I initially thought that my AGPS is not functioning as I didn't see any difference after doing a reset, it immediately came back with some satellites seen (even with the Airplane mode, so it was certainly not redownloading it). But in fact it seems that it actually gets cached in a way that the resets are not clearing it completely while the GPS is turned on. It seems that the only way to reset it fully and do a cold start is to reset it while the GPS is turned off (!). So, if I turn off GPS, do a reset, I also waited 20-30 sec and did a reset again, waited again, then turned it back on, it was now clearly doing a cold start and slowly started to pick up the satellites. I otherwise then followed your procedure, and presto, my GPS is solid again!
Now what I actually did that seemed to fix it (probably the above augmented reset procedure is the key) was that I had the phone in the car where I use it for navigation, started Waze, pulled up GPS status & toolbox (which shows its little icon in the status bar), and did the augmented procedure of #7 and #8, so in Airplane mode AND GPS off, I did an AGPS reset, then waited ~20 sec, AGPS reset again, wait 20 sec again (probably not needed, should need to test), then turned GPS back on -- NOW I could see it cold start and took minutes to pick up first few satellites enough to get the location, then little more to actually load the full sat data and show the 19-20 sats visible. I've never seen it pick up the position that slow, so clearly I was not able to fully reset the AGPS data.
After that, I seem to have stability back (the first obvious sign is that Waze reports close to correct speed, while before it was anywhere between close to the real speed and way, way lower, like reporting 24 km/h when in fact I was driving 50 km/h) and then no drop of GPS signal. I will test more to see how accurate it will remain.
My theory is that if the GPS module gets a downloaded AGPS dataset BEFORE it ever does a fix on it s own, it will be instable (in line with your procedure, you want to force a "clean" fix before applying AGPS data). When I did my spring update, as the upgrade did a full reset, I probably happened to use the GPS before the toolbox scheduled the download and refresh the AGPS data, while in the Aug upgrade it got AGPS before an unaided fix.
So, you may want to add that optionally you want to try the reset with the GPS turned off as at least in my environment that is the only way to fully reset it.