Personally, I understand the desire for a fixed price. But in this scenario surely it's quite easy to say something along the lines of;
There are a number of bodges and critical mistakes here. This isn't me scratching my belly and sucking my teeth, but it is likely I will uncover more. I can't predict what they will be or how long it will take me to correct them. For that reason this is my rate, [£]. At the moment I would expect it to be between [£x] and [£y], and if I discover something that will take it over [£y], then I will let you know so we can discuss next steps.
Personally, I understand the desire for a fixed price. But in this scenario surely it's quite easy to say something along the lines of;