Well, you do bring a smile!
Am I suggesting that David died and was resurrected? If you're talking about 'My servant David' then, yes, I believe he did die, and was resurrected. I believe all these Psalms are like parables. They lay the 'earthly' side by side with the 'heavenly'. If we have 'eyes to see' then we'll peer through the earthly window and get glimpses of the kingdom of heaven.
The same is true of Jonah. Jesus said, 'A wicked and adulterous generation seeketh after a sign; and there shall no sign be given be given unto it, but the sign of the prophet Jonas. And he left them, and departed'. [Matthew 16:4]
Your timing is a little off. David will not become king until the "last days", after the "sons of Israel will return and seek the LORD their God and David their king" (Hosea 3:5). The combined sons of Israel, the stick of Judah combined with the stick of Ephraim, have not been combined and returned to the land given to Jacob (Ezekiel 37). Only Judah, the Jews, have been gathered to the land given to Jacob, and David is not their king/shepherd (Ezekiel 34:22-24). (Ezekiel 37:24-28) & (Hosea 3:5) and no covenant of peace has been bestowed upon them (Ezekiel 34:25), as they are surrounded and pounded by missiles from their neighbors. First, all the nations (Daniel 2:45) will have to be destroyed per Zechariah 14:16, before the nations/Gentiles "worship the king", and keep the feast of Booths. Do you now keep the feast of booths, and when you don't, does your nation get rain? (Zechariah 14:18)