We had damage pretty similar looking and it came in through an aged butyl seal around a hatch door and window. Once the hatch door and window were removed it was obvious they were the culprit of the leak. My husband was in a huffy mood and ripped through the luan board. We were not able to find a matching luan board so we had to paint the entire interior which was fine with me since I didn't like it in the first place. He used a multi dremel tool like this one for cutting out rotten wood.
Dremel MM40-05 Multi-Max 3.8-Amp Oscillating Tool Kit with Quick-Lock Accessory Change Interface and 36 Accessories