Well the epic dialect was a shared kuntsprache utilised by all poets singing epic as well as later writers either consciously writing new literary epics or just Greek authors in general.
I'd say to be careful of authors like Apollonios in the sense that there is quite a bit of departure from traditional epic language and quite a few students find him frustrating and difficult, but well, well, worth it. It just won't be that easy.
You're obvious choices are Hesiod, though a bit more westerly in dialect forms. The Theogony is probably marginally easier than Words and Days, the Aspis is easier than both. You also then get all the Homeric Hymns, which are very very important in getting epic "down". You should definitely be supplementing your study of Homer with the hymns to Apollo and Aphrodite. Fantastic way to practice vocab, formula and syntax as well as charming compositions.
Remember, when they ask you whose are the best songs, reply that it is the blind man from chios.
Will not answer questions which only need a basic knowledge of grammar. Pay attention to the textbook.