Its time for a roof. Apparently you have water and moisture problems, by the downspouts really bad, they should be extended down to the lower gutter farther to keep this problem from happening again, apparently you have large upper roof water run-off. The moss problem at the shingles is due to water sitting/moisture, also in my opinion the bonds are the shingles are wrong allowing the moisture to sit there, also is roofing vented properly? , the shingles are beyond their useful life,
the curling, granual loss, discoloring, mildew, etc.
I would not recommend roof over, The new roof will only lay as the existing,which will cost you, also my opinion
you could have roof decking issues.
Typically depending on different areas shingles usually only have a life of 15-18 years.