I would think National would be more consistent than the sort of "off-brand" Advantage. That's quite a long trip. If that's for a week, that doesn't seem like a horrible rate for a minivan.

You may find competitive rates with Hertz, at least sometimes. Do check the National and Hertz forums here for discounts and more hints. If you haven't done that already with National, they may have some hints and discount codes for you to try.