And "sore kara" would indeed sound strange in this case (isu ni suwatte sore kara hon o yomimashita) because within a sentence after a "te" verb it generally has the implication of "finally" or "at last."
Something like: "Kyou haha wa ima o souji shitari kaimono ni ittari shite, hirugohan o tabete, sanji kara tomodachi no ie e ittari piano wo renshuu shitari shite, sore kara bangohan o tsukutte kureta." (Today my mother cleaned the living room, went shopping, ate lunch, from three o clock went to a friend's house, practiced the piano and finally made dinner.)
Although you could use just "kara" as a connecting preposition to emphasize reading the book only after sitting down.
(Isu ni suwatte kara hon wo yomimashita).