Good point.I'm glad you caught the error with the relative pronoun. Also you forgot the augment for ἀνέκριναν. You could also have used a participial phrase, τοὖ κηρυσσομένου αὐτοῖς τὸ εὐαγγέλιον. But either way works fine. It is also strikes me that one could also write οὗ, the genitive, by way of attraction with the antecedent, fairly common throughout Greek literature, including the NT.
ὁ λαὸς ανακρίναν ἀκριβῶς τοὺς λόγους τοῦ ἀποστόλου οὗ ἐκήρυσσεν αὐτοῖς τὸ εὐαγγέλιον.
Infact it sounds better this way.