You could just avoid the big banks and go for a smaller boutique that seeks to maintain its reputation with a companies first policy. The bigger banks are usually chummy with all institutional investors and will certainly pull shit to make a higher profit. An elite boutique bank, or a reputed banker running the show, can work wonders. For tech, one such bank is Qatalyst, for healthcare it's Centerview, like that, for instance. Even better if they can run an auction process for you.
That being said, the number of good "reputable" bankers is increasingly declining as they've soon realized they could make much more money on the investing side. There is a serious dearth of excellent bankers and a lot of mediocre bankers. This policy could not have come at a better time, if not earlier.