PayPal actually starts at 2.9% + $0.30 and charges a variety of add-on fees which you didn't include in your assessment: $30 per month if you want to design and host your own checkout pages, 1% cross-border surcharge if you want to accept payments from another country, 3.5% transaction fee when your customers pay with American Express, $0.30 per uncaptured authorization, a fixed fee portion of the original transaction fee when you issue a refund ($0.30 for domestic payments).
They do offer volume discounts, which is why you're at a 2.2% rate, and Stripe also offers volume discounts to businesses on track to do $1MM per year.
I'm not sure what your current processor and merchant account provider are, but we often do similar assessments against their add-on fees and come out to be less expensive.