The second factor email was associated with my account, I could see reset codes come through which were relayed to her but would result in an 'oops, something went wrong'. My guess is a bug due to account age / whatever.
I figured we had enough evidence to obtain a password reset, so I googled for gmail support contact details. There are none.
I then tried repeatedly to contact Google via twitter, all my tweets were ignored - probably because I only have like 20 followers.
In the end, my mother ended up porting her old mobile number to a prepaid sim, as $previouscompany had disconnected the number entirely, and used that as the second factor to reset the account.
Pretty damn frustrating that Google doesn't have any unpaid inbound support _AT ALL_.
Next time I'll consider paying a twitter influencer to impersonate me (or my mother), or paying for adspace, or using a mail service that exposes at least some form of support.