Hot air---you have an error in your numbers. The numbers only jive if the sizes are
205/55 and 225/50. You have 205/50 and 225/55.

Assuming 205/55 and 225/50 you are right, they are the same diameter. They will not screw up any computer period. There COULD be an interference issue with the wider 225 tire, but not likely. You can figure this out by inspecting the vehicle including lock-to-lock checking the front and allowing for some suspension travel, but I would be willing to bet it's fine.

The problem is the factory doesn't specifically spec the 225/50 as a sub, so the lawyer-driven tire shop won't do it.

They will if you bring the wheels in OFF the car though, and don't tell them what they are going on.