Post: First read the previous post. Should the words be בְּרָדְפָם אַחֲרֵיכֶם or בְּרָדְפָם אַחֲרֵיהם? The Septuagint supports our Masoretic text:
4 καὶ ὅσα ἐποίησε τὴν δύναμιν τῶν Αἰγυπτίων, τὰ ἅρματα αὐτῶν καὶ τὴν ἵππον αὐτῶν, καὶ τὴν δύναμιν αὐτῶν, ὡς ἐπέκλυσε τὸ ὕδωρ τῆς θαλάσσης τῆς ἐρυθρᾶς ἐπὶ προσώπου αὐτῶν καταδιωκόντων αὐτῶν ἐκ τῶν ὀπίσω ὑμῶν καὶ ἀπώλεσεν αὐτοὺς Κύριος ἕως τῆς σήμερον ἡμέρας,
4 and what he did to the host of the Egyptians, and to their chariots, and their cavalry, and their host; how he made the water of the Red Sea to overwhelm the face of them as they pursued after you, and the Lord destroyed them until this day;
So too, the Samaritan text, as we can see in Vetus Testamentum. However, it turns out that there are Masoretic variant texts which corresponds to the midrash mentioned by Chizkuni and Radak. From the Hebrew variants listed in Vetus Testamentum:
This would, perhaps, support the idea that this is a derasha made on a variant text, rather than other proposed answers.