I've found my problem!
The readings were correct, the problem was an app. Strangely I haven't seen any wakelock, but there surely is something plain wrong with it.
First I've put the phone in airplane mode - everything in the log seemed fine! 1 to 3 mA every minute. That's why I decided to dig deeper in the apps.
With the help of Greenify I've hibernated all the apps that were active - Facebook, Facebook Messenger aaaand HD Widgets. After that there weren't any mA spikes as in the first screenshot. Than I've checked the network usage in BBS, guess which app was first in the list. I've uninstalled HD Widgets and now I am running healthy 1 to 3 mA usage in deep sleep.
So I guess, my question is resolved. My advice - don't use the app.
Edit: Oh I forgot. Just to be sure, I've installed HD Widgets once again and the mA usage spikes appeared again, uninstalled it and they were gone. So it's definitely that app that's causing high battery drain