I have had to do several appeals with UHC on types of insulin. Those appeals were very easy compared to some of the others.
You can record the “day 3” issues for a few weeks and provide documentation for the appeal. I had to “use” crappy no-name insulin for 30 days and then explain how it did not work as well as the other insulin, and the appeal when through with no problem. And that was with UHC.
It helps to have an endo on board with you. If you explain the difference you are seeing with Humalog and NovoLog on day 3, your endo should be able to help with the appeal. If not, maybe consider getting an endo with a bit more “fight” in him.
There are a bunch of threads on TuD about day 3 issues if you want to read about them. There are a bunch of these types of threads.