The FAA " English proficient" is only Level 4! Being proficient does not mean you are good enough for level 6. Besides, the remark on your FAA is not dated, which is required by ICAO, since level 4 is only good for 3-4 years
The FAA actually check for
Level 4 or better, they just don't discriminate; if you pass, you pass. Recurrent checks are done (implicitly) every time you do a biannual flight check, instrument check, checkride or medical - all instructors, examiners and FMEs are required to inform the FAA if they consider your English proficiency is not good enough for level 4. Does that happen in practice? I don't know.......