Written on another forum and updated after further input; edited again on 12/29/17.
1) 1 Peter 2:5 suggests an ongoing progression that started in the first century CE and evidently continues now: 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 obeyed the Torah: the production of a royal priesthood would take place by adherence to Jehovah's law (mediated through Moses). But the law (Torah) would lead Israel 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.