Hi, I did a lot of different firmware for openwrt-based systems, also for OM2P-LC. Incl. custom splash page. So I still have a OM2P-LC around for testing.
_But_: As you want to use some google servcice, this will need to open access to google in the walled garden.
Which has the consequence, that android devices will assume, WAN connection is open, and _not_ start the small popup, telling the user, that some activity is required.
(I have a special trick, to fix this problem, but for vanilla openwrt systems, only).
Why not to use facebook-login, for example ? Possible to get email adrs, and something more :-)