Obviously a facial deformity doesn't prevent someone from working BUT we can't deny that disability discrimination isn't out there in the workplace. I've suffered from it directly myself and it's horrible. Was even told I 'look special needs'
(offensive anyway but more so because I do have SN). The same person also called me a 'spaz' and on another occasion, with a member of management, treated me to an "impression" of someone with CP, explaining in detail why they were {offensive words} because they don't have brains

I went home crying. I was also excluded from social events on the basis that one of my disabilities meant I had to have time off for hospital appointments, as I had that time off I was told I couldn't go a social event with work that week as I'd been allowed a half day to check my internal organs weren't breaking down.
In fact I've seen some truly horrific examples of disability discrimination, it shouldn't happen but it does unfortunately.
And having a disability can eat away at your confidence, I've met loads of other disabled people through Remploy and it's helped me a lot to know it's not just me in this situation. Loads of them have been called 'mongs' or 'morons' or the oh so charming 'retard' when they've been in the workplace.
Obviously I know I was very unlucky with my last job, I'm hoping the next person I work for will be decent, there are good and bad employers out there.
That's why I think something like Remploy would be a good idea for ProblemChild as they can help her in to permanent work with employers who don't live in the stone age. The OP has found temp work which is great so she's obviously got skills valuable to employers, plus work experience, so there is a strong chance of her getting a permament job, it sounds to me like confidence is the issue here.
OP - I really do believe you have a good chance of getting permanent work, it's a case of finding a decent employer who will only look at your skills, not what you look like. You could also look at 'two ticks' employers - they guarantee interviews for disabled candidates who meet the minimum requirements for the job (I know you don't consider yourself to have a disability but it would be a good way to practice interviews, especially with firms who have committed themselves to hiring a more diverse workforce).