I am surprised how worried and/or obsessed people are with their dates?!
As far as I understand your dates are only 3 or 4 days apart! I understand that you want the test as soon as possible as these tests are pretty worrying, but what difference will 3 days make? And why do you want to insist on a particular date anyway, because baby will come when he/she is ready.
My estimated dates were 8 days apart, but they reduced it to 7 so they wouldn't have to do any more testing. We are going with my scan date for now (which is the earlier one), so I can have as much care as early as possible. Baby is also measuring large for this date, so think this was a good idea. However if I go overdue I will push them to accept the other date as my EDD, so I will not need to be induced too early.
So all in all I think it is great to have to dates that are quite a bit apart as this gives you more options.
I hope things will work out ok for you and always keep in mind that these dates are only estimates anyway. If it is just about seeing the mw 3 days earlier, I am sure they can do that. I know that with my mw tests are not done on the day you are 16 weeks (or whatever you need to be), because she only does appointments once a week, so being that I am due on a Saturday I must have been 16+4 by the time I had my blood taken for the Downs Syndrom test.
Lana xxx