Yeah it's one of those things, and I'm of the (uneducated) opinion at this stage that we just don't understand our bodies as well as we think we do when it comes to how diet affects us. Have you checkout out Auto Immune Protocol diet? It's very hard to follow as it's a) strict and b) costly but it apparently is a game changer for skin conditions, and it all goes back to gut bacteria. There's also a lad on youtrube who very bravely documented his psoriasis and how he cured it with a raw vegan juice diet. You can see in all his videos how it definitely worked for him, but a diet of juice is a horrible thought for most.
I've done all the steroid creams, phototherapy(avb) and 3 years on methotrexate. I refused to do the biological injections as a potential risk was heart failure and I'd two mates die young of heart attacks at the time and it wasn't worth the risk. All the treatments seem to work, but at the same time you are aware that you are on something and they all feel like papering over the cracks.
In my case changing my diet was what sorted me out, after being told by specialists that diet wasn't a key factor. I cut out dairy and meat and my skin cleared up completely. I think it's a combination of that and the fact that my diet now is a whole food, plant based one, so I'm getting more nutrients, vitamins etc from what I'm eating. I'm convinced that in my case cutting out dairy has been the biggest factor. I don't think you have to go as extreme as a raw juice diet, as per the video you mention, but it wouldn't hurt to try cutting out dairy for a month to see if it makes a difference to you. Also trying incorporating some juice or more vegetables to your diet may be beneficial. I messed about for over 20 years, with GP's prescribing things that didn't help or in some cases made things worse, getting referred to dermatologists, paying to go see private specialists, having light treatment which helped temporarily but has it's own risks etc and the thing that fixed it was my diet.