Negotiate harder, and in USD.
Typically I will begin placing an order with two OTC desks at the same time, while also looking at exchange order books. I game the brokers against each other.
If it is a smaller order (5 - 6 figures) I will compare Coinbase Pro's fees with whatever my OTC desk is telling me. OTC has to be less than Coinbase Pro.
So thats how I pretty much guarantee a less than 1% fee.
$1bn = multiple OTC desks and multiple orders. The bitcoin market is much deeper than people think and gets deeper every day.