When you say 'possibly ex-batts' it sounds as if someone else had rehomed them first and then you took them on, is that right? In which case they were probably 3+ years old when you got them, as battery hens are usually culled after their second year in lay, and at this point a lucky few get rehomed. After this age, they slowly stop laying, or start laying weird eggs like the one you describe, or begin to lay eggs with thin shells or no shells at all, just membranes, or they get prolapses. Sadly this is a sign that their egglaying apparatus is no longer functioning properly, because they have been bred to lay so frequently whilst in their first two years that all their eggs have been used up. A hen is born with a certain number of egg cells in her ovaries, just like us, and releases one every time she lays an egg, and when they're gone, they're gone and she has reached the 'henopause.' All hens reach this stage eventually, though with purebreds it's often later in life because they don't usually lay so regularly in their early years so the egg supply lasts longer.
Nothing really you can do about it, i'm sorry to say, it's just inevitable ageing. In younger hens, abdnormal shells can be due to calcium deficiency, but in mature hens fed on good layers pellets this is unlikely to be the case, though hens at the end of laying maybe can't absorb calcium so well as when they were younger.
I agree with chris that she will be lonely on her own, though you also have to understand that it may be difficult to integrate her with younger ones. If you want to go on keeping hens, you had best get two or three rather than one, as the present hen may not last very long and then you will have the 'single lonely hen' problem all over again if you only get one companion for her.
my poor baby 
