And here's BDAG on τάσσω:ἀκούοντα δὲ τὰ ἔθνη ἔχαιρον καὶ ἐδόξαζον τὸν λόγον τοῦ κυρίου καὶ ἐπίστευσαν ὅσοι ἦσαν τεταγμένοι εἰς ζωὴν αἰώνιον
>τάσσω fut. τάξω LXX; 1 aor. ἔταξα; perf. τέταχα. Mid.: 1 aor. ἐταξάμην. Pass.: aor. ptc. n. sg. ταχθέν EpJer 61, pl. ταγέντα (TestJob 16:3); pf. τέταγμαι, ptc. τεταγμένος (Pind., Aeschyl., Pre-Socr., Hdt.+)
① to bring about an order of things by arranging, arrange, put in place
ⓐ of an authority structure pass. αἱ οὖσαι (ἐξουσίαι) ὑπὸ θεοῦ τεταγμέναι εἰσίν the (structures of authority) presently existing are put in place by God Ro 13:1 (cp. IAndrosIsis, Kyme on the role of Isis in ordering a variety of social, political, and economic structures; some interpret as metonymy for officeholders, cp. Da 4:37b; Horace, Odes 1, 12, 13–16; 49–52; Vergil, Ecl. 3, 60f); of established authority in contrast to a rabble MPol 10:2 (τάσσεσθαι ὑπό τινος as here, Eur., Iph. A. 1363; X., An. 1, 6, 6; 2, 6, 13; Simplicius In Epict. p. 60, 19 Düb. τεταγμένοι ὑπὸ θεοῦ).
ⓑ of a pers. put into a specific position, used w. a prep. τάσσειν τινὰ ἐπί τινος put someone over or in charge of someone or someth. (Polyb. 5, 65, 7; ins; Mitt-Wilck. I/2, 11, 51 [II B.C.]; PRev 51, 9 [III B.C.]) pass. (Arrian, Anab. 3, 6, 7 ἐπὶ πῶν χρημάτων=in charge of the finances; En 20:5; Jos., Ant. 2, 70; 7, 370.—ἐπί τινι Ath. 24, 3) ἐφʼ ἧς (i.e. the way of light) εἰσὶν τεταγμένοι φωταγωγοὶ ἄγγελοι B 18:1.—On ἄνθρωπος ὑπὸ ἐξουσίαν τασσόμενος Mt 8:9 v.l.; Lk 7:8 s. ἐξουσία 4 (τάσσεσθαι ὑπό τινα ‘be put under someone’s command’ Polyb. 3, 16, 3; 5, 65, 7; Diod S 2, 26, 8; 4, 9, 5; OGI 56, 13 [237 B.C.] τοῖς ὑπὸ τὴν βασιλείαν τασσομένοις; but Just., D. 126, 5 ὑπὸ τῷ πατρί).—τάσσειν τινά εἰς assign someone to a (certain) classification, used also w. an abstract noun (Pla., Rep. 2, 371c, Polit. 289e), pass. belong to, be classed among those possessing ὅσοι ἦσαν τεταγμένοι εἰς ζωὴν αἰώνιον Ac 13:48.—τάσσειν ἑαυτὸν εἰς διακονίαν devote oneself to a service (cp. X., Mem. 2, 1, 11 εἰς τὴν δουλείαν ἐμαυτὸν τάττω; Pla., Rep. 2, 371c τάττειν ἑαυτὸν ἐπὶ τὴν διακονίαν ταύτην) 1 Cor 16:15.
② to give instructions as to what must be done, order, fix, determine, appoint (Trag., Hdt. +; ins, pap, LXX; TestJob 17:3; Just., A I, 17, 1 φόρους, A II, 5, 2 νόμον; Ath., R. 14 p. 64, 19 τὰ φύσει τεταγμένα)
ⓐ act. and pass., foll. by acc. w. inf. (X., An. 3, 1, 25) Ac 15:2; 18:2 v.l. περὶ πάντων ὧν τέτακταί σοι ποιῆσαι concerning everything that you have been ordered to do 22:10 (cp. X., Resp. Lac. 11, 6). ὁ τεταγμένος ὑπʼ αὐτοῦ δρόμος the course which has been fixed by him (i.e. by God) 1 Cl 20:2 (cp. Philo, Poster. Cai. 144, Rer. Div. Her. 97 τεταγμέναι περίοδοι ἀστέρων). κατὰ καιροὺς τεταγμένους at appointed times 40:1 (cp. Polyb. 17, 1, 1).
ⓑ mid.=act. (Hdt. et al.; 2 Km 20:5) εἰς τὸ ὄρος οὗ ἐτάξατο αὐτοῖς ὁ Ἰησοῦς (i.e. πορεύεσθαι) Mt 28:16. ταξάμενοι αὐτῷ ἡμέραν ἦλθον they set a day for him and came Ac 28:23 (τασσ. ἡμέραν as Polyb. 18, 19, 1; Jos., Ant. 9, 136).—DELG. M-M. TW.
>>Arndt, W., Danker, F. W., Bauer, W., & Gingrich, F. W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed.). Chicago: University of Chicago Press.
>>Exported from Logos Bible Software, 2:32 PM February 24, 2019.
In the context, Paul was approached by gentiles, begging that Paul would preach the gospel to them. He directed the to reconvened the following sabbath to hear the preaching.
Arndt, W., Danker, F. W., Bauer, W., & Gingrich, F. W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed., p. 991). Chicago: University of Chicago Press.
... is there any chance that τεταγμένοι refers to that arrangement? "those who had been directed [to reconvene] believed into everlasting life"?
I notice it used similarly here:
ⓑ mid.=act. (Hdt. et al.; 2 Km 20:5) εἰς τὸ ὄρος οὗ ἐτάξατο αὐτοῖς ὁ Ἰησοῦς (i.e. πορεύεσθαι) Mt 28:16. ταξάμενοι αὐτῷ ἡμέραν ἦλθον they set a day for him and came Ac 28:23 (τασσ. ἡμέραν as Polyb. 18, 19, 1; Jos., Ant. 9, 136)
Arndt, W., Danker, F. W., Bauer, W., & Gingrich, F. W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed., p. 991). Chicago: University of Chicago Press.
---Matthew 28:16 οἱ δὲ ἕνδεκα μαθηταὶ ἐπορεύθησαν εἰς τὴν Γαλιλαίαν εἰς τὸ ὄρος οὗ ἐτάξατο αὐτοῖς ὁ Ἰησοῦς
Alternatively, since usage #2 is "to give instructions as to what must be done" might it read:
"and as many as had been directed [by Paul], believed - into everlasting life"
Or perhaps,
"and as many as had been directed [by Paul] to everlasting life, believed"
?