As a general rule, my morning BG levels are higher, similar to Kenny's. When my hba1c test came back as 32 in November last year, down from 83 on the previous test, my morning readings were still in the 6.x range. Even now, like Kenny said, my first thing in the morning readings are still the highest of the day.
As other's have said, my advice would be not to worry about it. It's the result over which we have little/no ability to influence. Overnight our stomachs completely empty, resulting in a sense of hunger or needing to eat. Our primitive monkey brains translate this as needing to go out and hunt, which needs energy, so the liver dumps glucose into our systems to provide that energy boost - having no appreciation for the fact you're not going to be fighting lions and running around hunting, you only in fact need to traverse a flight of stairs and the short walk to the kitchen! It's a physiological response to an instinctual situation, and it's called "dawn phenomenon". People experience this to varying extents, but as T2 diabetics then our insulin resistance means we're less efficient at processing the liver's glucose dump. In turn though, the liver is oblivious to insulin resistance, it knows nothing of it, so it receives the instructions to dump glucose and dutifully performs that action. The good news though is that a) keto making your liver dump it's reserves of glucose isn't a bad thing in the mid-long term, and b) if you notice your BG readings continue to climb in the morning then this can generally be resolved by eating a small low/zero carb "breakfast", such as a boiled egg for example.