Judging by what I see (especially in the third pic), I would remove the everything from the roof and strip the EPDM. From that point it will be easy to determine how much of the roof and structure is rotted, which is probably a lot more than is visible. Removing the roof will also make it easier to replace the header over the slide.
As I have rebuilt quite a few rotted roofs and walls I would attempt this repair without hesitation, but that's me. It's not worth having repaired professionally, unless you have deep pockets.
You could hack it together and you might get a few years out of it, but if you have the ability and can rebuild it correctly, it should give you quite a few more years of use.