Dude the shiny spots are no big deal.
I often had the best uniforms in my squadron when I was in the AF. I used to soak both my top and bottoms with a whole can of starch, hang them in the shower, and the next morning they would almost stand up on their own. Then the next morning I would spray starch on the crease areas while I was ironing. They would be so stiff that I HAD to spray a little more to get them wet and to loosen up enough, or else they were difficult to crease.
Seriously. Unless you used some kind of weird starch and the shiny is really really fucked up, its no big deal. One trick you can use in the future is to starch them the night before. Then the next day, if you want to put on a little while ironing, spray it on the inside instead of the outside.
The only difficulty with the way I used to do it is that when you spray it on right before ironing, you get white flakes. They can be brushed off though.
YMMV, but everybody I ever knew who took the time to starch their BDU's good and stiff in the AF had a little bit of shiny spots. Usually all of my creases would be a little bit shinier then the rest of the uniform.
If you really want them gone, try soap and water. You might have to wash them. I don't think its a big deal, but YMMV. I used to put a SHITLOAD of starch on my uniforms, and you really had to look close, in just the right light, to see the shininess.
I don't think it detracts from the uniform IMO. YMMW