This is an interesting thread to read. I looked at the link @4castle provided, Wescott's comments, as well as several other articles. I searched the Bible in the original languages to find a similar pattern to help explain why it's translated nearly always as, "Your throne, O God, is forever..." rather than how Wescott suggests, "God is your throne forever..."
There is an important aspect we overlook on this passage in Psalms, and it's mentioned in the original post: The NT authors applied this part of Psalm 45 to Jesus, thereby bringing this passage into the category of a Messianic prophecy or Messianic passage.
Because the NT authors, under the guidance of the Holy Spirit, applied this verse directly to Jesus, the verse in Psalms needs to be interpreted with that hindsight as well. Even though the Psalmist may not have realized the Messianic application to the words he wrote, the Holy Spirit knew and ensured the Hebrews author brought it out in the NT text.
It is in this light, therefore, that nearly all scholars translate the passage in Psalms as, "Your throne, O God, is forever..." rather than the way Wescott and the NWT renders it.
I looked at least 10 English translations - including the 1599 Geneva Bible, the Orthodox Jewish, the Expanded, Young's Literal, Complete Jewish, Amplified, Lexham English, RSV, NASV, ASV, Douay-Rheims 1899 American versions - a Spanish, Portuguese, Italian, and French version as well. They all either rendered the passage, "Your throne, O God, is forever..." or a similar syntax. These different versions provide a glimpse of the scholarly opinion of this passage.
Translation teams from 400+ years ago, as well as today, from different countries, and under different supervision have consistently translated this passage, "Your throne, O God, is forever..." Knowing that scholars take into consideration not only the words, grammar, and historical syntax, as well as letting the Bible interpret itself (like viewing an OT passage in light of the Messianic application or fulfillment), it is clear to see what Biblical scholars believe to be the most accurate translation of the passage in Psalms: "Your throne, O God, is forever..."