I wanted to be able also to give some relevance to fabric coating of control surfaces, but if I enable that group of layers, only a series of black holes appear, and previous trick doesn't work.
Of course, the patent, wise-ass answer would be "just get Photoshop and be done with it", but since I'm not a wise-ass (usually) I'm not going to say that.
I'm suspecting it might have to do with a blend mode or layer style that Emel used on the fabric effect that might not be supported by GIMP. I've never used GIMP, so I don't know for sure. But I did download the template (he did do an awesome job, like you said) and I can have a look-see to determine if that might be the cause. If so, I can maybe do some alpha tricks and merging to get it to look as Emel intended without using any additional layer attributes that GIMP may not support.
Give me until tomorrow and I'll let you know if I can prepare something for you to try out.
UPDATE: I had a couple minutes so I took a look at the template. Emel used vector shapes with layer styles to create the fabric effect. I use shapes a lot, too...they're handy and Emel knows all the cool tricks that make your work go faster but if he's like me, he probably doesn't have GIMP compatibility in mind when he's being creative.
Nevertheless, I just rasterized the layers for you so GIMP should be able to digest them. PM me your email addy and I can shoot you off a small PSD file with the layers.