Very odd. First she tells you that the broker would give you your membership number. This does not sound right. Usually when somebody tells me something that is incorrect, I figure everything that they said is probably incorrect. This has been a pet peeve of mine from the time I bought my first contract. Why these member services representatives are so against doing there jobs is beyond me. Their job is to provide members with service. Once they give you a membership number (or possibly once the deed is recorded) you are a member and they are being paid by members to take care of members. If they don't want to take hundreds of calls per day, then they need to figure out a better way to handle it and telling people to wait 30-40 days is not it. Remember, it is their job to take care of members and they are doing whatever they can not to take care of new members. This is on them, not you.
Call your broker and ask them if they know of some new law that would prevent Disney from giving you your membership number. Your broker should be a licensed real estate agent and should know the laws.
BTW I never did get a letter with my member number. If I would not have called, I would have never gotten it. Now that being said, it did take 2 weeks after it was filed before I did get the number by calling.
Good luck and congratulations on your new
DVC.