Why don’t you try to omit each day one of your usual habits? For example, you could decide to work a couple of hours before looking at your mails. Another day start work an hour or two before having breakfast and so on. The thing is that when you do those things later, they still take the same amount of time, the question is at what moment of the day you are working at your best. I guess it’s more difficult to handle if every day it’s at a different moment of the day. One needs then to keep improvising on the order of stuff to do and it gives a certain element of instability (which is interesting nevertheless).

These sorts of in-between moments are everywhere in life, and the hope is always to make something out of them rather than simply to let them pass by. It's a difficult thing to do. I always think of the fact one hears quoted that we only use 10% of our brains. What happens with the rest? Do we not know how it is used, or is it simply empty space? A room without empty space is not livable...

There is a nice couplet in the Tao te Ching about how a pot is made out of clay, but the hollow space inside is what makes it useful. Maybe we also need "down time" in life. If so, part of what is important is simply not being frustrated when this happens.

At the same time, I sympathise with the frustration of having to do "mindless" work at a time when one feels very awake. I am not sure what to suggest to make it more enjoyable. Perhaps trying to become more efficient, even by twenty minutes or so, could make a difference?