Can I make a retina iPad display websites at full resolution? In other words, can I make it appear to the web server as if the device is 2048x1536 pixels and device-pixel-ratio 1?

I'm happy to pay for an app that does does this if there is one…
I believe this could be a problem with how sites are interpreting the User-Agent string and are assuming that it's an older iPad / mobile device.

Try using the Google Chrome browser and it's "Request Desktop Version" feature.

https://itunes.apple.com/ca/app/chrome/id535886823