They should always go by your own LMP dates or your dating scan if you had one will be the most accurate.
Don't let them change your EDD based on subsequent scans, as the growth rate of all babies differs greatly after about 12 weeks.

Do you know the actual date of your LMP AND the day you O? Or just the LMP?
Remember that you may not ovulate in the middle of your cycle, and the egg may not have been fertilised until a day after O, so that would explain the initial variance in US and LMP dates.

Like I said though, I would take the date that allows you to be as late as possible when delivering, which from what you are saying I think is your original LMP date.

Why do they want to induce you though? Is there a medical reason? ("Big baby" isn't a medical reason lol)