Slimming world I would swear by. You'd never go hungry on it. I was on it last year but had to stop due to illness and since changed my diet. However, I still follow Pinch of Nom on Facebook which is a couple of member's recipes in line with the Slimming World diet. I have tried a good few and loved them, there are a fair few sweet recipes too.
You mentiond low carb, low sugar and I'd recommend it with high protein and veg, I'm currently doing it whilst eating full fats too and still losing weight in a non extreme way - it's recommended for GDM so it's been more out of necessity for me but I'd continue it. As long as you have a healthy heart, I can see why it works for so many people. I eat 3 meals a day as well as 3 snacks and never really go hungry since getting to grips with it. Fwiw, I think it may be similar to the Atkins diet but I've never done that.
Both require lifestyle changes though, the might not be as quick for an initial kick start. Although saying that, with slimming world I had a 5lb loss the first week - I think it totally shocked my system!
If you are going to do Slim Fast, my aunt told me Tesco do UltraSlim which is apparently near enough the same but cheaper and you can follow the same diet plan as you would slim fast.
I think whatever diet you go for it's going to be trial and error to some degree - you might have a bad week, you might not change one week or you might notice after the initial period you don't lose anything at all, it's what works for your own body. My friend has Joe Wicks books and loves them, maybe also for the pics!? You've got to have something that inspires you though!
As long as you have the support you need, Pumbleton, it'd be horrible to think that you're having to bottle things up as opposed to you just not wanting to talk about it.