Sorry Danielle but that’s hogwash and another excuse.
Living together won’t change diddly…it will be even worse because he’ll be there and just as tired.
One of my best friends had a husband like this and it does NOT get better in fact it usually declines and pretty soon you’ll be lucky to get it on your anniversary or BD. Do NOT move in until its fully addressed and sex has improved. Sorry but NO MAN is THAT TIRED to have sex, whereas not once in any relationship or even my husband of 20+ years ever told me he was “too tired”.
For instance (one of many) my ex husband had a 20 hour flight from Qatar (middle east), an hour of out-processing and then a bus ride to where everyone was waiting from them to arrive after a 9 month deployment. Within three hours of his arrival we were getting it on, initiated by HIM, then he slept for like 12 hours lol.