If you don't know the car biz, or even if you do and don't have a fleet contact, AAA has a buying service that will also get a you a fleet deal.
Dealers are professional negotiators, so it pays to know what you might be able to get. Edmunds can be a big help with that. There's about two thousand profit in the cars at MSRP.
BTW, $2200 off is not $1000 under invoice. Unless you're talking second sticker which I've seen still around from time to time. That practice more or less went away in the 80's. :