Ok, as @sec-con alludes to; more than one way to skin this puddy-tat.
By adding my domains as hosts, and then forcing my network connection to use DNS of the ipfire first, I have forced the resolution of the domains to be the local 10.0.2.x range and this works; bypassing the hair-pinning altogether.
I just need to then alter the wifey’s laptop to replicate that singular network connection change, and all will be well in the world again.
Thanks for humouring me, guys.