Is there any way to ignore INSTALL_FAILED_VERSION_DOWNGRADE on application install with the Android Debug Bridge?

It appears the latest version of adb tools has an "allow downgrade flag" that isn't shown in the adb help, but it is shown in the "pm" help on the device. So use: adb install -r -d <link to apk>

You can try and use adb uninstall -k <package> and then installing the older apk. From the adb usage guide:

  adb uninstall [-k] <package> - remove this app package from the device
                                 ('-k' means keep the data and cache directories)

I've tried it myself with my apk, and it seems to work for most of the data (some data like RawContacts was not saved)

Did you enabled Multiple account on your device (and push your apk via ADB)? If so you have to remove the apk in every account. After complete uninstall, your push will be OK.