You're looking to buy 1000 bitcoins... On a forum... For $7 million+.
Honestly, why don't you just use an exchange? You're willing to pay 1% when most exchanges would charge <0.25%. If you're not willing to give an exchange proper KYC documents why would you be okay with giving it to some random on the internet? Also, most people would want to charge a much higher fee for a (somewhat) anonymous buyer. It doesn't make sense.
You have 0 rep here, and you say you have an escrow that you would like to use. Who exactly is the escrow? If it's not someone known around here we'll have to assume it's either you or a friend of yours.
Sending in small batches means nothing when a small batch is 100 Bitcoins.
If it sounds too good to be true, it probably is. Always stay skeptical with your digital cash people.

Maybe you should meet up with this guy:
https://bitcointalk.org/index.php?topic=4311387.0If you were familiar with bigger OTC transactions you would know that most sellers are willing to offer a discount for that big of an amount. So if you take that in account as well as slippage on most exchanges it actually make sense for both parties to agree on a price based on the spot on a arbitrary exchange at a given time. I understand that there is a lot of scammers hanging out here but the process I described above is as transparent as it can be. If you would like to know more feel free to send me an email