Things like this make me hope - just a little bit - that my cats never get over their agoraphobia. (Yes, truly, agoraphobic cats. It takes immense effort to get them to put a whisker out of doors never mind a paw & they press themselves flat to the floor the whole time we're out. Unless they scramble up me & cling to me in blind terror, that is. As soon as we go back into the house they bolt away & hide - usually under my bed - and are on edge for ages afterwards. Am hoping nicer weather might make the garden seem a more inviting prospect. But I digress.)
Any kind of cat-thievery is grim but this does seem extra-foul as they obviously knew she was your cat. Even if they'd somehow never noticed her before they stole her, as soon as the posters went up, if it wasn't cat-napping but a genuine Let Us Give The Poor Cat A Home thing, they'd've been round to you saying "We May Have Your Cat". How could they be so selfish & so cruel to your family (inc TillyCat)!? Ugh.
Do find it genuinely boggling that so many people think Cat Commandeering is okay - &/or apparently have no idea what a stray cat looks like nor what the appropriate thing to do with a Found Cat is! one of my friends has a cat who, once she's seen my pal off to work in the morning, gets her C19 Lady On & bops about Paying Calls. My friend was a bit startled to be stopped by a woman while out walking accompanied by cat. Initially she thought there was Cat Confusion as StrangeWoman addressed Cat as NotCat'sName, only to be told "oh, no, we know she's called Cat'sName, but we call her NotCat'sName because we think it suits her". This was followed by a lengthy speech about the Special Bond Cat had with StrangeWoman's Offspring as Cat would sit on Bump whilst StrangeWoman pregnant so Offspring recognised Cat immediately & will love at forever etc. StrangeWoman tops list of suspects for keeping Cat in when Cat doesn't wish to be kept: Cat's routine involves escorting my friend back home again from where she drops her in morning & paying only v brief calls if friend at home so... There have been Odd Happenings with Cat's collars, too, beyond her having squiggled herself out of them, I mean 
Another friend is in the awkward situation of a neighbour's cat wanting to move in. Said Cat is elderly, rather scraggly & had fleas when she first appeared through my friend's catflap. After investigating, friend discovered cat belonged to a neighbour. Cat is shut out for much of day (& night) and is one of a number of animals in the household that give impression of getting minimal care. My friend no longer feeds Cat, having talked to Owner, but still allows Cat in (& has de-flead more than once) as Cat so desperate for somewhere soft&warm to sleep - and for attention&affection from a human, too. Cat often spends nights there as preferable to neighbour's expectation Cat will spend night roaming neighbourhood.
This is obviously not similar to either of these sorts of things, unless your cat had a nervy b &/or developed amnesia in the style of a ridiculous soap opera & moved next door as a result. It is catnapping
Pure And Simple, unless TillyCat is an undercover agent & has been on a top-secret mission for the last 11 months. Which I astrongly suspect isn't the case, somehow...
Poor TillyCat must [have] be[en] absolutely miserable being kept imprisoned in your neighbour's house. Is particularly awful she & her sister were separated & won't get to be re-united. Really REALLY hope that this is all sorted out - with happy ending for you & the TillyCat - as soon as possible. Ideally with the cat thieves being punished. Even if you do get TillyCat back once the police have stepped in I think you should still approach the media. These people should be Named And Shamed.
Have everything crossed for you - let us know if you get a reply to your letter, won't you, please?