>the cost should be built into the price

This doesn’t make any sense. So the price should include potential transaction fees for the most expensive method of payment? Or you want the cheap payment method to overpay and subsidize the expensive payment method?

There’s also usually a flat fee plus a percentage, how do you bake that into the advertised price when the flat fee may be spread across multiple items? Should every item increase in cost by $0.30 or whatever?

This is just stupid. Advertise the cash price. You can go to an atm if you don’t want pay the fees associated with your preferred payment method.