F. Coulmas uses this text as an example in Writing Systems (Cambridge, 2003: 129). The caption ('Ionian Greek inscription'), transcription (e.g. ἐλθόυτος and ἀλογγόσο̄ς), accentuation (e.g. ἢλθον) and translation ('The foreigners guided... and the Egyptians Amasis') are all sadly faulty.
The non-Ionic nature of the main inscription is evident from several features:
Ἐλεφαντίναν, Ψαμά̄τιχō τοὶ, and ἁμὲ. Note also πρᾶτον in the mark of Anaxanor.
Anne Jeffery's notes (search for 'Abou Simbel') are very informative about the variety of texts that compose this single 'inscription'.
LSJ cites this inscription in at least six entries. A search for 'Abu Simbel' returns ten instances.
LSJ s.v. ἵημι: 'Dor. ἀν-ίη SIG 1 (Abu Simbel, vi B.C.);' [my bold]
s.v. ἀνίημι: 'Ion. 3sg. ἀνίη SIG 1 (Abu Simbel, vi B. C.' (sic) [my bold]
This use of eta is also seen in ἦλθον and ἦχε. LSJ relates the latter to ἄγω, but then the eta would have to be an Ionic feature.
(On the basis of the drawing in Coulmas), the name Ψαμμά̄τιχος (Ψαμμήτιχος in Hdt.2.2.1, etc.) shows the (familiar) Light Blue use of <Ψ> for p+s and for /kh/, not the Red use of these characters for /kh/ and k+s respectively.
LSJ s.v. Ψ notes, 'not used in the Attic alphabet: in the Western Gr. alphabets it represents the sound χ (kh): with the value ps it is found in SIG1 (Nubia, vi B. C.),...'.
The key point in understanding these spellings is that (this) Rhodian script, like (some) Cretan, used
ΝΕΣΤΟΡΟΣ, ΠΟΤΕΡΙΟΝ (ποτήριον), and KENON (κεῖνον, κῆνον).
See Buck § 4.6 for eta in use to represent a vowel outside Ionic.
The mark of Telephos of Ialysos, one of the Rhodians illustrates this: Τήλεφός μ’ ἔγραφε ℎο Ἰᾱλύσιο. The toponym on which the ethnic adjective is based appears in Homer in its Ionic form, Ἰήλυσος (Il.2.654: Λίνδον | Ἰηλυσόν τε || καὶ ἀργινόεντα Κάμειρον.).
Note also the name Ἀναχσάνορ (unless Ἀναξσάνορ: SEG XXIX 1669) and his mark ℎο Ἰᾱλύσιος ℎόκα ('Dor.' for ὅτε) βασιλ|εὺς ἤλασε τὸν στρατὸν τὸ πρᾶτον.
The adverb υἷς 'as far as' is only in this inscription (according to PHI Greek Inscriptions): Cf. Buck § 132.4 'Rhod. ... (no. 104.3)'.
κατύπερθε (apparently only here in epigraphic texts) shows psilosis and is called 'Ion.' in LSJ. Indeed, it is in Ionic (50x Hdt., 1x Arrian's Indika), but may not be unique to Ionic. We must remember that Rhodian has ἰαρός and ἰερός with a smooth breaking (Buck §§ 58.b 261.8: ἐπ᾿ ἰερέως 'of NN' appears as a dating formula), which suggests some degree of psilosis.