You can use a trick devised by
@Dellabrown. Download the app store version of Chapters, and sign in using your Google account. After that, delete the app store version (without signing out) and install
@Sbenny's mod. After that you should be able to sign in with your Google account. You may have to try the above process a couple of times, including rebooting your phone if the first time didn't work.
The first time I used the trick, it worked perfectly from the first try. The second tome, I had to attempt it thrice but eventually it all worked.