Time for an update. Ginny has suddenly had an epiphany - J is not out to get her!
She's always been a bit uncertain about him, although at first she would sleep on the bed with us, and cuddle up to us both on the sofa, when the weather turned warm and she preferred to be on her own bed, she became a little wary of him. It's also obvious she's had bad experiences in doorways - likely at the shelter - as she's always been really nervous of getting into confined spaces like hallways, entries, gates etc with us. She would take a wide berth if she wanted to get past him and if he made any sudden moves, she would flinch away.
Since J has been back from the couple of weeks he spent in Andorra, though, she's been brilliant with him, and it keeps getting better and better. She will turn from me towards him if he calls her, and will even run towards him when she sees him on walks. He's been giving her all her meals and always high value treats, and she seems to have finally clicked that he's one of the good guys. Even to the point that she will walk in the gate past him when he opens it. Before, it was always a bit of a dance to open the gate, walk away from it, let her through far enough that he could walk around her and close it again without her freaking out.
Happy days!