The cool thing is that these modules come with 2MByte of i2c flash, rather than the usual 512k. And that might just be the source of the problem.
I wasn't aware these modules existed and immediately ordered a pair. Despite the fact that the German postal service is on strike, the modules arrived on Saturday.
The weekend was rather busy, so I couldn't test drive the modules. From the first look, I am impressed by the build quality and the nicely readable silkscreen. So impressed in fact, that I'll mount the headers upside-down to have an unobstructed view of the print.
One thing I didn't like at first glance was that to change to flash mode, I need to change soldered jumpers. With the number of tries I need to get things right, I considered mounting a switch.
A closer look at the schematic revealed this:
Now that's nice circuit design! I can still use a jumper cable on the breadboard to tie GPIO0 to GND manually to reflash the firmware.
It went better than I expected. See here.