small gaps in the graph can be because the BG levels are changing rapidly the Libre just can't hand it.
Thanks for the AGP graph, and the rough daily routine. That is amazing that you don't or didn't have ANY hypos during the day but then again you're pretty much always over target
Could you try having breakfast pretty much as soon as you're up, before going to work? What do you have for breakfast? Do you pre-bolus at all? What are your injection sites like? It's almost as if all the insulin you inject during the day does nothing until you lie down! The only thing I can think of is at rest your liver does the grab back but with no insulin on board it shouldn't consistently drop you that low (as if our bodies always do as they should!). Thats a mighty monster roller-coaster you're on.
What are your Insulin to Carb ratios (I:C) like? How many carbs do you have at each meal?
Just looking I'd say your breakfast ratio needs increasing but that may also because of starting at a high BG - some T1Ds find the higher they are the bigger the correction dose needs to be.
Can't remember if you have tried or if it's already been suggested to do a basal test? could you post an agp of the time since changing your basal dose to the morning only please?
Sorry so many questions!