I can join this club, i just started on a pump and noticed that i have to significantly up my basal overnight to keep my morning sugars low. Weird thing is that when i was on Lantus i NEVER had this issue.
I think the only thing you can do is up your long acting a bit, and go to be on an empty stomach with sugars in the low 5's... try that a couple nights and see if you can at least get a routine down where you wake up and bolus a bit to get it down.
So far i have been waking up to see BS in the 8s and immediately injecting to try and get that down ASAP, before doing anything else.