@Oxterguff it is worth bearing in mind very few schools will give negative feedback on applications. I do think it's worth showing it to someone senior you trust for really honest feedback.
I think it's difficult because a lot of people (in part due to poor pay or lack of staff) start taking on additional responsibilities a lot earlier, so in some ways, someone on UPS3 who hasn't taken on that responsibility before isn't so attractive to schools. They may wonder why you've never taken on that sort of role before and if you really want it. I'd perhaps specifically address this in your supporting statement.
Something like a lead practitioner role could also be a good fit, perhaps.
This is going to sound harsh, but including pension contributions etc, you cost about £20k more to employ than someone on about M3. ECTs are a bit different because having too many ECTs is difficult now. With schools so financially stretched, you don't just have to edge out the competition, but show that you would be significantly better than them.
But honestly if you aren't getting interviews for a shortage subject (around here, schools will often interview every applicant, as usually there's < 5 anyway) then I'd be seriously questioning if your application is as good as it can be.
Or else perhaps in your area, your subject isn't as shortage as you think. Is there somewhere you could commute to (eg expensive city?) Which might struggle to recruit more?