Andrew wrote:

I think this is mistaken. Hebrews 9:23-28 describes what Christ, the great high priest, does in the heavenly sanctuary when he ‘appears in the presence of God on our behalf’. This metaphor controls the whole paragraph. His first appearance in the sanctuary was to offer himself as a sacrifice to put away sin (9:26; cf. 9:11-12). The writer to the Hebrews, fearing that his readers may be in danger of losing faith (cf. 6:11-12; 10:32-39), urges them to be patient because Christ will enter the sanctuary a second time, will appear in the presence of God a second time - ‘not to deal with sin but to save those who are eagerly waiting for him’ (9:28). This is not a second coming to earth - it is much more like the coming of the Son of man to the throne of the Ancient of Days to receive a kingdom on behalf of the suffering saints of the Most High.

While I somewhat agree with your conclusion that "This is not a second coming to earth - it is much more like the coming of the Son of man to the throne of the Ancient of Days to receive a kingdom on behalf of the suffering saints of the Most High" I find the path you took to get there somewhat convoluted.

The Material in Hebrews explaining His high priestly role is based on the atonement in Leviticus 16.

While it is true that the high priest had to appear twice in the holy of holies (before the mercy seat), it is also true that he had to appear twice before the people.  Thus, for Jesus to adequately fulfill the typology it was necessary that as high priest He must take His blood into the holy of holies (first appearance) and sprinkle His blood upon the mercy seat.  That being done, He must appear before the people (first appearance) to declare sins forgiven.  That being done, He must then take the kid that was selected "for the LORD," sacrifice it and take its blood into the holy of holies (second appearance) and sprinkle its blood on the mercy seat.  That being done He must then appear before the people again (second appearance).

Now, ostensibly this is the way that all those things actually worked out to fulfill the type in the first century.  Jesus, the Prince and Savior (Acts 3:14, 5:31) sacrificed Himself on the cross and was resurrected to become the high priest - as the high priest He then ascended to the Father and took His blood into the holy of holies and sprinkled it on the mercy seat (first appearance, John 20:17ff).  This being done He came out of the holy of holies an appeared before the people (first appearance, John 17:19ff) and identified the "kid" "chosen for the LORD" ("those looking for Him") and returned to the Father (second appearance, ascension, Acts 1:9-11) and functioning as the high priest; presided over the sacrifice of the "kid chosen for the LORD" (Rev 6:9-11).  When the sacrifice was completed by the killing of those "that should be killed…"  Jesus took the blood of the sacrifice into the holy of holies and sprinkled it on the mercy seat (second appearance) and appeared the second time before those who were "looking for Him" (Col 3:4; 1Tim 6:14; 2Tim 1:10, 4:1,8; 1Pet 1:7, 5:4; 1John 2:28, 3:2; et al.) This final event is the Parousia.  It is the coming of the resurrected Son of man and the resurrected "kid" sacrifice (the first century martyrs, cf. Rev 20:4) coming into the kingdom of heaven.  Upon the Parousia (both second appearances as one) the scapegoat was sent into the wilderness  (Rev 17:3) where it was destroyed (Rev 17:16-18).  Ostensibly, the metaphor used within the NT to represent the "two kids" of Leviticus 16:5, 7-10, et al. is the two sons of the two women of Galatians 4:22 or something like that.

Perhaps, the following verses (emphasis added) best explain the finale presented above:

When Christ our life appears (in glory), then you also will appear with Him in glory. (Colossians 3:4 NKJV)

I charge [you] therefore before God and the Lord Jesus Christ, who will judge the living and the dead at His appearing and His kingdom: (2 Timothy 4:1 NKJV)

Finally, there is laid up for me the crown of righteousness, which the Lord, the righteous Judge, will give to me on that Day, and not to me only but also to all who have loved His appearing. (2 Timothy 4:8 NKJV)

And now, little children, abide in Him, that when He appears, we may have confidence and not be ashamed before Him at His Parousia. (1 John 2:28)

that the genuineness of your faith, much more precious than gold that perishes, though it is tested by fire, may be found to praise, honor, and glory at the revelation of Jesus Christ, (1 Peter 1:7 NKJV)

when the Chief Shepherd appears, you will receive the crown of glory that does not fade away. (1 Peter 5:4 NKJV)