The old HP 4600 series type of see through flatbed scanner is still the best way. I still do this.
I've scanned entire playfields and entire cabinets very successfully stitching with Photoshop Elements.
As already noted, the amount of overlap of scans is very important for any stitching effort, including photographs. Too little and it doesn't work well. Too much is never bad.
If you can find a flatbed scanner that can work upside down (I've never found one but some people say they exist) that will work too.
The flatbeds I have only support the scan bar on only one side, gravity keeps the other side on the rail. Turn them upside down and they are crooked and jam.
As a last resort you can do good scanning with a camera using the same overlap rules and a fixed camera to object distance. But it needs a lot more distortion correction and scaling in Photoshop. A lot more work.