In just focusing on this one phrase...."David shall
never lack a man
to sit on the throne of the house of Israel"....and trying to set aside the timeline or narrative you've believed....how else can you interpret that other than to say that has to be the spiritual kingdom (because... as you've pointed out....it clearly didn't play out that way on earth)?
There is also this passage in Hebrews 8 that contrasts Christ Jesus's priesthood with the ancient Levitical priesthood in ancient Jerusalem (Jesus, Melchizedek, and David were all priestly kings):
Hebrews 8
1The point of what we are saying is this: We do have such a high priest, who sat down at the right hand of the throne of the Majesty in heaven, 2and who ministers in the sanctuary and true tabernacle set up by the Lord, not by man. 3And since every high priest is appointed to offer both gifts and sacrifices, it was necessary for this One also to have something to offer.4Now if He were on earth, He would not be a priest, since there are already priests who offer gifts according to the law.