I can’t see any “if” statement here so they can’t be 3rd class conditionals
For verse 13 - Μεχρι seems to take a subjunctive as seen in BDAG, which would make sense as a possibility and not a statement that we definitely will reach that unity
as a conjunction until (B-D-F §383, 2; Rob. 975) μ. καταντήσωμεν Eph 4:13 (cp. Hdt. 4, 119, 4; SIG 976, 71 μέχρι ποιήσωσιν; PCairPreis 48, 7 μέχρι τὸ πλοιαρίδιον εὑρῶμεν; TestSol 9:8 P; SibOr 3, 570. On the omission of ἄν s. Mlt. 168f; Rydbeck, 144-53). μ. οὗ w. subjunctive (Herodas 2, 43; 8, 8 [Cunningham reads μέχρις εὖ in both]; POxy 293, 7 [27 A.D.] μέχρι οὗ ἀποστείλης Da 11:36 Theod.; EpArist 298) Mk 13:30 (μ. ὅτου v.l.); Gal 4:19. μ. ὅτε (ὅτου v.l.) Hv 4, 1, 9; GJs 10:2 (s. B-D-F §455, 3).
Ινα takes a subjunctive as the mood of the verb in the clause it introduces, hence the verse 14 example
Verse 15 I would read as a hortatory subjunctive - exhorting us to action
Of course, I could be wrong
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