Fire door handles.

[cheddarman]

The handles of the fire door between my garage and kitchen just keep falling off.
The wood between the handle fixture and the actual mechanism is so thin that screws just won't tighten before coming up against the metal. Shorter screws are just too weak to support the handles and the wood is now basically destroyed.
Any suggestions as to how I can secure the handles please?

 

[cheddarman]

I am still hoping there is a carpenter or similar out there who can help me sort out this door??