Yet, Jesus was 30 when he began His ministry and ministered for 3 and 1/2 years. That would make Him 33 and 1/2 years old in March or April... pushing back His birthday until August - October range.
I think given what Luke says that the conception was near or on the 25 of our December. That would then make the date of His birth in sometime during our month of September.
I agree with the range you describe.