If your conception calculator is correct, guy A. How do you know your due date, was this all done by calculators online from your period? If so, you can't know anything for sure. They are just based on averages.
If you happened to have gotten an ultrasound in your sixth or seventh week and did not tell the doctor when your last period was (so he was not influenced by that) and he told you the due date, it might be more reliable. But otherwise guessing based on online info is not going to help you split the difference with these dates so close together.
Doctors and calculators all based on lmp
See above where I answered in the "Comments" box. Don't use your first day of your last period over ultrasound results to begin the count, women have their periods and ovulation whenever their bodies feel like it and do not do so based on the calendar or when an app tells them to. If you have ultrasound evidence, use the ultrasound evidence even if it disagrees with when your period last came.