What gestational age were you given for the embryo on June 26, did they tell you a "weeks and days" figure for the pregnancy on that day? Do you still have a copy of the ultrasound? It might be printed on it.
Do you know for sure what she meant when she said "I was measuring a week ahead"?
And, when you say that on July 17, the midwife looked at your ultrasound, was the midwife looking at the ultrasound from 6/26 or did you have a new ultrasound?
No, just look for a number like CRL, in millimeters.
I have to leave for a while (sorry, it's a volunteer site, and I've got to do something). Will get back.
OK, well, here is some of my thinking. There really is only one puzzle in your story, and that is, why the doc said you were a week "ahead," if that is the exact word she used, when she read your 6/26 ultrasound. According to the numbers above that you have confirmed are written on the ultrasound, it didn't indicate that you were anything but right on track. If she could see an embryo size on the ultrasound that you can't see, and felt that it conflicted with the rest of the numbers, it seems like she would have said this was why you were supposedly a week 'ahead.'
Was "ahead" your word or her word? You're taking it to mean "go back in time on the calendar one week and say conception was one week earlier." Was that because your midwife told you to do this, or was this something you did after she told you something else? Because (as you have explained) you didn't have sex at the right time for conception one week earlier to make lots of sense.
If we assume she was right, this gives you two areas to evaluate. One is to re-check everything based on hard data, not on memory or assumption. To do this you need contemporaneous records and the ability to remember exact words the doctor used and to sort it out from what you understood the doctor to be saying. You would also need all the dates you had sex to be confirmed from something (bills for products, calendar, app), and also to be certain you didn't forget to write one down.
Trying to understand why you got three exact dates that match that seem to be from three separate ultrasounds can be tricky. Here is what *might* have happened, but you might never have any way to confirm.
If a reliable, relatively early ultrasound is done, many doctors never change the due date, even if later ultrasounds suggest a different due date. This is actually good medicine, because growth rates can diverge from the average over time as embryos develop, making the first ultrasound the most on target for determining an estimated due date. If your doc or midwife has had a lot of experience with this fact, he or she might simply have made the rule that the first EDD is the best EDD, even if a later ultrasound would give a different EDD. This would mean that the second and third ultrasound having the same EDD would not be independent confirmation.
As I said, always using the first ultrasound is usually the sensible approach. The only time it is not, is if the first ultrasound was off for some reason. But she apparently said what she did about your supposedly being "ahead" early in the process, before your second ultrasound. So you still need to know why she said it even if you write off the second and third ultrasound's EDDs as meaning anything useful.
If you have already given your midwife pushback on the question of dates, she might just think this is the patient seeking reassurance and would just say nice and reassuring things, which would mean you won't get serious help with this question. Doctors don't love to be questioned, and don't always remember why they said something 15 weeks ago, and in fact might stick by their story rather than saying they made a blunder. So you would have to be super tactful and super clear, if asking why your midwife said what she did 15 weeks ago when reading the 6/26 ultrasound. To do this, you need a clearly marked calendar of the dates of sex, so she can see what you're getting at. But I don't give you more than a 50/50 chance of hearing what you need to know to understand her thinking back then, even if you went in and did the best presentation of the problem ever.