I'm happy with the result and wanted to share it:

Here's the template of the file:

You can preview what it looks like, and play around with it, here: http://xmas.bitligo.com
You probably shouldn't use an online version. If anyone needs a how-to how to adapt the cashaddress.org offline html file to this, then let me know.
The SHA256 hash of the changed html file is: 1643530a4d4c814497c33172c9eb59895e349499e8c84cb848f49a566151071a. It has two changes: the graphic for the paper wallet is changed, and I have changed the QR rendering code so that it only prepends 'bitcoincash:' on the Bitcoin Cash Address, but not on the Private Key QR code (otherwise the Bitcoin.com wallet doesn't recognize the Private Key when scanning).