You may just want to offer an additional piece of hardware that lives on site and does the same logic as the web-based piece (everything's just forwarded to you

You may just want to offer an additional piece of hardware that lives on site and does the same logic as the web-based piece (everything's just forwarded to your backend systems for processing), only stores data if their internet is down (with the ability to control how cards are authorized, as in up to $x auto authorize if internet's down and eat the cost later if it fails, or deny all, etc.). I think this would integrate well with the hardware options you have and would provide another sell-point without a large amount of effort. The trick is, they buy the hardware, not the software. The software is still a service that is provided (or you can have a more expensive plan that includes onsite hardware, in which case you own the hardware even though it's at their site).