I would change up your meds. If taking your thyroid medication at night works better for you then OK - but the T3 Cytomel at night is not good. You are on a synthetic medication so it requires the body to convert the meds into the proper proteins to get your body working again. I believe you being on this cycle of taking meds at night has changed your natual body pattern and that is why you are off. You could try keeping your Synthroid at night and moving your Cytomel in the later part of the morning. I guess around 11 am. What time at night are you taking it?
Another thought could be your adrenals are tired. If you were/are hypoT for a long time - the adreanls are forced to work very hard to try and keep up with the imbalance. They eventually will become off too.
The symptoms you describe are very common in fatigue of the adrenals. A cortisol test - blood and even better - saliva test could tell you if this is an issue.
Cortisol that is off will give a thyroid patient the fatigue in the morning (if low cortisol) and give you a bump in the afternoon to evening (if the levels change)
My energy has been best in the afternoon too. I wake up alert in the mornings, as in not sleepy, but my body barely moves. I pretty much flop onto the couch with a coffee the first few hours of the day. Any errands or visits are usually done in the afternoon. Then, I find I'm much sleepier in the evenings and go to bed earlier than I normally did.
(I'm just on Synthroid and TSH was 4.84 at last test)
I would have thought that taking your Cytomel at night would rev you up and keep you from falling asleep.