reinforcing cabin roof

Hi everybody, I have 30 foot boat (Fastwave 30).
Previous boat owner decided to make the sliding part of the cabin entry of carbon. The carbon is thinner, so he made also a thinner sliding slot slimming down a cabin roof. That was not so clever decision because the winches on the cabin roof under load are bending the cabin. Not much, but enough to make a reinforcement. The poorly made modification is not waterproof and there are water leaks in the cabin.
I have carbon fabric unidirectional 300g, airex 80 10mm, and epoxy. I will put two pieces of foam longitudinally 120 cm long and 15 cm wide starting under the winches. I know that the density of airex is not enough, so I suppose that backplate will be necessary. I need advices about layers in sandwich and what to use for a backplate.
Thank you in advance

 

Pictures would help a lot..

Airex can be formed with a heat gun to some extent, or you can put it in a heat box and get it hot enough to form and conform to the inside of the roof. Locally cut out the airex and replace with wood and bond it all in.

 

Skip the Airex and just bond a piece of G-10 to the underside of the bases and through bolt.

 

Thank you for your answers.
this was initial "state". I have removed lower part and the backplates. Not an easy job because the part with backplates was laminated (Fein multimaster helps me a lot).
I was thinking to put on each side a piece of Airex longitudinally 120 cm x 15 cm (this is the length of the lower part) and glue/fasten the lower part back. No need to preform the foam. If there is no need for foam, how many layers of carbon?

@Par I don't know what is G-10, pls if you can explain I am newbie

 

The laminate schedule for your chainplates needs to be calculated, especially if using carbon. G-10 is a machine pressed laminate with a high fiber/resin ratio. It's very strong, inert, machinable and though considerably heavier then a carbon plate, it's just one piece, bonded in place, no muss or fuss or figuring out how many layers of fabric. A 19 mm (3/4") thick 305x457 mm (12"x18") sheet of G-10 will be about $150 (retail). Just epoxy it in place and call it a day.