I have worked with many other nationalities, and as a native English person, with no real accent, can only add the following:
I appreciate the second language complications, and normally speak slower, and use a limited vocabulary and avoid slang, try to keep to one topic at a time.
I have been fortunate to have flown with many Russians, both in the cockpit, and worked them on the ground and in ATC. It would be reasonable to say their level of English was 2-3, my Russian 0-1.
I am now in Middle East, and still use the same approach, speak slowly, and clearly, and listen to the responses.
Several of the level 4 qualified persons I work with should not be level 2. The purpose of the test is to try and ensure that apart from the cockpit English, they can communicate around the aviation environment.
A problem that even level 10 !!!! will not cure is that when problems occur we always think in our base language, and as such are stressed to translate into approved ICAO English.
At the moment I do fly in a mixed nationality flight deck, and the problems are obvious, we have different understanding of primary procedures. He is American and I am English.......
The problem is the same language, but different interpretation.
glf