I agree - I think if you take this job you need to shift your meds to meet the demands and stay on track with it everyday as the same.
It is probably most important to take synthroid at the same time and in the same way every day (meaning with water every time or with coffee every time or with food every time if that's the way you take it).
Synthroid is pretty long lasting, it takes a while to build up in your system when you start taking it, and it takes a while to "wear off" when you stop taking it (just ask any of those how had to wait and wait for their levels to drop before they could have RAI). If you happen to miss a single dose, I doubt most people would notice a difference.
I think your worry about sleeping after taking it might be valid, as I often have a hard time going back to sleep after taking mine an hour before I get up in the morning.