Thanks so much for your response!
The app does have responsive design, and if the app is already launched, it works as hoped:
If I launch another app first, and then try to launch the Cordova app by choosing it to slide over, it's width is the device width, so it's chopped off on the right.
If, however, I launch my Cordova app first, then launch another app, then slide over the already opened Cordova app, it formats for the narrower width properly.
There was a viewport meta tag which set the width to device-width, but I took it out and it made no difference. For some reason when it first launches on being chosen as the app to slide over, it thinks the width is the whole screen.