Written on another forum and updated after further input:
1) 1 Peter 2:5 suggests an ongoing progression that started in the first century and evidently continues in the here and now (21st century): καὶ αὐτοὶ ὡς λίθοι ζῶντες οἰκοδομεῖσθε οἶκος πνευματικὸς εἰς ἱεράτευμα ἅγιον ἀνενέγκαι πνευματικὰς θυσίας. . . (NA28)
2) Exodus 19:4-6 seems to communicate the idea that Israel had the opportunity to become a nation of kings-priests, if they proved obedient to the Torah. The production of a royal priesthood would take place by means of their adherence to Jehovah's law (mediated through Moses), it appears. But the law (Torah) would lead them to Christ in harmony with Galatians 3:24ff.
3) In the case of fleshly Israel, I see the kingly and priestly offices as likely compossibles if they proved obedient; at the very least, some natural Israelites would have been perpetual kings in the nation and others would have constituted age-abiding priests. Compare Isaiah 49:6-7; 61:6; 66:21-22. But all hinged on their acceptance of God's Son.
4) It's quite likely that Peter is alluding to Exodus 19:6 along with other passages in 1 Peter 2:9-10--maybe the apostle has Luke 22:28-30 in mind also. But the words of Psalm 110:1-4 seem primarily applicable to the Messiah; he then arranges for his anointed followers to be joint-heirs with him into perpetuity.
Of course, I hope it's understood that this is how I perceive things now. I'm willing to be corrected.