Good attempt, Anangelaway. Sorry I focused on the use of tenses, not the adequacy of the words. In practice, though, there is no problem saying:
" chaque jour, je m'endormais tard et me réveillais tôt",
although we might want to revert the entire thing and say:
"chaque jour, je m'éveillais tôt et m'endormais (or me rendormais) tard".
J-J