It seems to me the "term" spiritualizing gets thrown around while failing to see that Peter did exactly that in Acts regarding David's throne/tent.
(Acts 15:16-17 After this I will return, and I will rebuild the fallen tent of David; I will rebuild its ruins and restore it, so that the rest of humanity may seek the Lord, namely, all the Gentiles I have called to be my own,' says the Lord, who makes these things)
The above is from Amos:
(Amos 9:11 "In that day I will rebuild the collapsing hut of David. I will seal its gaps, repair its ruins, and restore it to what it was like in days gone by.)
The Gentiles were being called "my own" when Peter stated the above, therefore the only conclusion is Peter is claiming a "spiritual" fulfillment of Amos. Now I'm not saying that all prophecies should be "spiritualized", but Peter has set a precedent here.
He further states that David's throne is heavenly and not earthly:
(Acts 2:30 So then, because he was a prophet and knew that God had sworn to him with an oath to seat one of his descendants on his throne)
(Acts 2:33 So then, exalted to the right hand of God, and having received the promise of the Holy Spirit from the Father, he has poured out what you both see and hear.)
(Acts 2:34 For David did not ascend into heaven, but he himself says, 'The Lord said to my lord, "Sit at my right hand.) etc.