Herodot 2.124 ("τὴν ἔδειμαν ἔργον ἐὸν")

I have two questions about the following sentences (Herodot, Histories, 2.124.3) :

The workers working for the pyramid of Cheops... ἐργάζοντο δὲ κατὰ δέκα μυριάδας ἀνθρώπων αἰεὶ τὴν τρίμηνον ἑκάστην. χρόνον δὲ ἐγγενέσθαι τριβομένῳ τῷ λεῷ δέκα ἔτεα μὲν τῆς ὁδοῦ κατ᾽ ἣν εἷλκον τοὺς λίθους, τὴν ἔδειμαν ἔργον ἐὸν οὐ πολλῷ τεῳ ἔλασσον τῆς πυραμίδος. ὡς ἐμοὶ δοκέειν.

[my translation]

They worked in teams of 100,000 people, continuously, each team working for 3 months. As for the time spent by the people exhausting themselves, the time necessary to make the road along which they pulled stones, it seems to me that it was 10 years; they built the road, a structure that was not, by far, less than the pyramid.

my two questions

• (question #1) "αἰεὶ" in "αἰεὶ τὴν τρίμηνον ἑκάστην" may modify "ἐργάζοντο" (→ "They worked continuously") but also "τὴν τρίμηνον ἑκάστην" ("→ "... each team working continously for 3 months"). Is there a way to choose between these two interpretations?
• for the sake of completeness, the singular "ἑκάστην" in "αἰεὶ τὴν τρίμηνον ἑκάστην" is normal; see e.g. Iliad 18.495-496.
• (question #2) Why is "ἔργον" an accusative ? Is it an apposition to "τὴν" in "τὴν ἔδειμαν ἔργον ἐὸν" (→ "They builed this [road], [it was] a work being...") ?
• For the sake of completenesse, see here for "πολλῷ τεῳ" (dative of τις).

Any help would be appreciated !