i have namechanged to post this as i don't want to be id in RL but i'm a reg.
In answer to your question, i would say you are most certainly NOT being unreasonable in wanting to do LL or something similar. As someone who spent over a decade being 12 stone overweight, i can really really understand that this sort of weight brings huge emotional problems and i felt pretty desperate most of the time.
I think the important question, though, is whether doing LL or something similar will have the result that you want, (which i presume) is to lose weight and keep it off.
The only way to do this long term is to mend the destructive relationship you have with food.
You say in your post "I have tried diets such as slimming world and weight watchers but the results just arn't quick enough and I fall back into the same bad habits".
How is LL going to stop you falling back into these bad habits??
For several years i ran a post weight-loss support group in the London area and i was always surprised by the number of LL member who would walk through our door until i found out that the lady who ran the local LL group was suggesting that they come- because she didn't know what else to suggest to help them.
These were people who had been though their programme and had received their group support, but it hadn't resolved the underlying issues.
Be really honest with yourself: Do you think you know how to cope with life without using food as a crutch?? If not, that is where to start.
I've now been slim for ten plus years-i never weigh myself and don't think about food very much. I certainly don't have good and bad foods or foods that call out to me from the fridge any more. This is becuase food isn't a crutch for me anymore, it is just food.
Please, please don't sell yourself short by letting the weight loss industry con you into thinking if you just change the food then you will magically change into being someone who can cope with life without food issues.
Sorry for the very long post and if i come across as being bossy, my heart went out to you when i read your post and i wanted to help. I wish you happiness and freedom