But I solved it and kinda came to your solution anyway:
(a) it bothered me that /etc/gdm3/greeter.gconf-default was being replaced, so I did a search to find what would be doing that
(b) found some interesting stuff that Debian should be doing but is not doing cos the Mint sysdev guys have put in these 'adjustments' for whatever reasons; the first clue was in the README located in /etc/linuxmint/adjustments
(c) from there I found that '15-gdm3.overwrite' was the key cos it contained
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(d) so it was simply a matter of editing the first linuxmint greeter file cos it replaces the gdm3 one
(e) and yay... it provides what I want!