Hi ericam, this is pretty much the same for me. I didn't get my first scan til around 19 weeks, when I was given EDD of 20 June - and an impossible conception date, as I was in a different country to DP!
My LMP gives me a date of 27 June, and if I work it out from conception date - like you, I am 100% certain of the date! - it would be 25 June (so I'm over now whatever date I pick!).
At my booking in appointment, the mw asked which date I wanted - I chose the 20th - mostly because of work issues/mat leave - and also to give myself the option of 'early' induction if things were getting too much. So they weren't too bothered about the date at that point I think.
Anyway, my notes still say the 20th, and have had a few mws telling me that I would be booked for induction by the 30th (today), but I've stuck to my guns - had a good chat with doc last week, and am going to see them again tomorrow.
Don't forget you can refuse any treatment, and ask for monitoring and expectant management, which is what I'm going to do (and I'm having my first sweep tomorrow). If there's any risk at all, I'll go for induction, but I'm not going to be scared into it if my baby just needs a little more time to get himself ready!
As Starlight says, conception date could be slightly different, as egg and sperm can both hang around - but it wouldn't make your date any earlier, it could only be later.
Good luck!