Not what you want to hear, but the only real answer is to reshoot without the glass in front of the original. If you look closely there is a lot of glass reflection on both the left and the right sides, and removing it manually is extremely time-consuming and tedious high-precision work. You will need to use adjustment layers and masking, and paint the correction in gradually.
It is possible to photograph originals with glass, but then you need cross-polarized light - a polarizer in front of the lens, and then polarizing sheets in front of the light sources rotated at a 90 degree angle to the lens polarizer. This cuts off nearly all reflected light, but also reduces total exposure by about three full stops. This is really only practical with flash units. The heat from halogen bulbs will melt the polarizing film.
I would second what D Fosse said. If you manually retouch. Using Camera Raw's dehaze works fairly well with some reflections, but it is a lot of work. Cross polarizing filters work great. I have a set, which I do use with strobes, mainly to avoid camera shake. I do have quartz modeling lights, which have causes some rippling of the filters, but hasn't melted them. But then they're not real high wattage bulbs.
Attached is my polarizing filter. You can see the ripples that the heat has caused. I've been using these particular filters for over 35 years.
To add a try... you can duplicate the layer and play with curves or contrast to make it darker. Then screen back the layer till it looks similar. Then use the clone stamp tool to try and blend the hard lines and hot spots. But if you can shoot the picture again with out the glass like D Fosse said it would be the quicker way.