I didn't mention 1% as idle guesswork, I have direct knowledge of several businesses paying close to 1% on online (card not present, no signature) transactions. I'm not saying its easy to negotiate good rates, but its possible, even for fairly early stage startups. I got 1.6% for a startup turning over only about $20k per month, no track record and 'non standard' business model.
So feel free to push your bank, get quotes from their competitors, they can almost certainly do better for you.
EDIT: I just notice that stripe is planning to introduce volume discounts - that would make a very nice product!
I do about that volume, mostly card present, and think I have decent rates. I think I'm at Interchange plus .2% plus 1 cent per transaction plus $20 per month, and end up around 2.7% for total fees. I'm sure one can do better, but not by a lot. I'm willing to bet a considerable sum that you are not actually paying 1.6 percent once it's all added up. But if somehow you are, the loss of the bet would pay back quickly if I could get those rates myself!
Key scaling issue is pricing. 2.9% is fine for low volumes and no risk validation, but once you're turning over large volumes and have a track record of no chargebacks etc the comparison looks much worse. If you can offer businesses a pricing that 'scales' with substantial reductions in transaction fee by volume then there is a growth path, otherwise any business would be crazy to stick with you no matter how good your service and APIs, etc because 2.9% could be half their gross margin and they can get 1% by dealing with the bank direct.