Just a note for future - she told you 2 weeks, so why did you email after 1 week? For me (a new long arm quilter) I might not even have started your quilt at that point, and still be planning to meet the 2 week mark. I don't like being bugged - at least not before the agreed upon date. That said - she should have told you when she got behind esp. since you were obviously eager to get it back, and asked if the delay was an issue for you.
I would not think that in general people send quilts to LAQ for speed, however. I'm sure in most cases you could do it faster/sooner yourself. The LAQ is used because they can do something you can't - either because of the size, or the intricacy of the pattern, or whatever. Generally it will take a little longer than doing it yourself - because you aren't their only client.
In this case, you could simply say no, the end of the month is not sufficient and you need to drop by to pick up the quilt.