This is a technique I recently discovered for reducing glare:

1. create a selection using the lasso tool around the area of high glare
2. use the shadows/highlights adjustment and reduce shadows to 0% and increase highlights to the desired level

For cases of intense glare this may need to be repeated a few times.

Note - this technique doesn't work in all situations. I tried this out on six designs and it worked perfectly on 4 of them, but didn't work at all on the other 2.