"Once you express strong interest in getting bought, you've just lost all negotiating leverage. "
Sure if you maintain that strong stance. But you can always change your level of interest and the opposite party will sense that and run to fix the deal. It's a game of chicken at that point but here's the thing. The acquirer is only looking at you and has decided they want what you have. If they didn't they wouldn't be attempting the acquisition.
So look as eager as you want. And then stop being prompt and act as if something else is going on and watch and see what happens. The investment banker doesn't want to loose a deal.