first, a couple of things. is your period normal? always 28 days cycle? do you know the conception date?
i imagine they first told you oct 4 only based on your last period. now for me, i knew the exact date of conception which was 8 days later than they were saying. the doctor kept using my LMP, so when i went for my first ultrasound, they told me i might be miscarrying, and when they went to look for the heartbeat on the doppler, they couldnt hear it. even though i explained i ovulate late, we used OPKS, and my husband was out of state the week they thought i conceived, they still used the earlier date causing me unneccessary worry and followups. after the heartbeat issue, they officially changed my due date to what i told them which was exact on the babys development by all their tests. so last periods arent a sure indicator unless you ovulate day 14 every month and have 28 day cycles, which many woman dont.
that all said, if you had had an early ultrasound, they are reliable since fetuses have developments at specific times those early weeks. like a fetal heartbeat or yolk sac only happen within X days of a pregnancy. so if you had an ultrasound at 6 weeks, i would put alot of stock in the date they gave. when you get to be as far as you are though, there are easily discrepancies of 2 weeks in terms of estimating a due date, so its just not as accurate in terms of due date.
sooo, unless you know the date of conception, i wouldnt necessarily say the original date was exact since you didnt have an early ultrasound. if you are someone who doesnt feel comfortable to be forcibly induced unless you are 2 weeks late, i wouldnt even worry. due to the second ultrasound equaling your measurements and being in the middle, maybe thats the safetest to go by. but i would still make sure to have the baby by october 2, that way it will either be on time or 2 weeks late. (i personally would never let a baby go 2 weeks late because of a friends experience, but thats a personal decision. if it were me, i wouldnt go past the 25th since there was a possibilty that would make you 1 week late) for you, i would just make sure not to go past october 2nd since if the sept 18 was correct, infant mortality goes up after 2 weeks late. it would just be better to be safe. and if october 4th was correct, the baby would be right on time minus 2 days.
but im still betting on that you ovulated later, and werent really due october 4.