You're all so active! And I feel so slow to give an update... But today I managed to get to the garage, drain the coolant, and run with distilled water a couple times.
The pic of original coolant is in the pic - looks greasy!

The foam at the radiator cap is from the 1st round with water.

And the video is from the 2nd attempt:
At times, it looked like some smoke coming out the radiator - if it is fumes then the diagnose is clear I guess. The rich foam didn't come back at 2nd attempt, although it all still looks very dirty.
Unfortunately, I had to rush back home - but for me it looks like there is too much goo in all the system and it wants to get cleaner. I am thinking about one more flush with distilled water, then filling it up as it belongs with coolant and take it for a short spin around.
I also took off the expansion reservoir to give it a cleanup.
The pic of original coolant is in the pic - looks greasy!

The foam at the radiator cap is from the 1st round with water.

And the video is from the 2nd attempt:
Unfortunately, I had to rush back home - but for me it looks like there is too much goo in all the system and it wants to get cleaner. I am thinking about one more flush with distilled water, then filling it up as it belongs with coolant and take it for a short spin around.
I also took off the expansion reservoir to give it a cleanup.