Repairing Edge Rot

Hello,
I have a detached garage that had lost several lengths of drip edging...and water creeped in. The rot is 12 - 18" up the wood for several stretches of 6'. The joists appear soild with a probe.

Is there a way to repair this without totally removing and replacing the shingles? Like some trick to roll to roofing back? Maybe that's just wishful thinking?

Thanks,
John