(1) Either use Yochanan and Yeshua or John and Jesus. If you're going to be affected, use the complete affectation.
(2) His approximate timing of John's birth is based on his unproven assumption that the Abijites served at Sukkot.
As you conceded, your source does not prove that the Abijites did Temple service on Sukkot. So he hasn't proven his date for John's birth, and therefore he hasn't proven his date for Jesus' birth, either.
John's papa would have served in the temple in june. Nine months later is passover. 6 months after that is sukkot. John was probably born around passover, and Yeshua was probably born around sukkot.