Back in the day, those 377/5s came off the back of a Southern order and only went to FCC out of necessity. When it was clear these weren't going to go back to Southern in time, along came the order for the /6s and /7s.
I think the plan was very much for these units to return to Southern when FCC/Thameslink were done with them. This just wasn't able to happen as soon as originally planned.
What will probably happen now is the 35 377s currently being used by Thameslink will soon return to Southern, allowing a similar number of 377s to be handed over to Southeastern to help alleviate the stress on their stock. Some of those TL 377s are already used by Southeastern on a PPM basis to cover certain PM Rochester and Ashford services, which only goes to show how desperately they need them.
Sorry to say jamieP, but I believe Class 377/5 is correct here.