PODs permitted at any point after his ascension to the crown.
Edit: The challenge is for Richard to leave England better off after his death than at the time of his ascension to the crown. How this occurs is up to the responder.
Now where does this say anything about him being a good king?

Why not make the sibling feud worthy of the Byzantines or an episode of Jerry Springer.
So, Richard eludes his captors, but to throw others off the trail accepts the suggestion of the person who protected in a harrowing attempt. Some fear that Richard was killed (it was a peasant who looked similar) and so rumor has it that Richard has died.
John takes voer the crown and begins taxing the people. He also orders the imprisonment of Eleanor and Arthur, who Richard learns of and frees ina tense battle. (If you feelt he need ou can have 1-2 of them die, too) John is disliked becasue of his imprisoning such young folk by some,a nd because of his taxing by some.
Richard shows up and he demands the crown back. John has won enough nobles to his side that a bloody fight ensues. John is killed, Richard badly wounded. However, he lives long enough to mold Arthur and marry him to Isabella of Scotland. The two had children,a nd whent he rest of the Scottish line dies out, there is a clear English claim on the Scottish throne; some might claim independence but it should hopefully go easier than OTL.
(Note - I almost had it 100 years too early for the Scots, where a 3rd son of the king was going to marry Eleanor, who would then be queen, and a union formed, but alas, that was the early 1100s, not early 1200s)