How about giving your civie some treats while you're testing. I tend to think there's some vying for attention going on.
When you're able, it can help to not always test at the same time. We don't actually know if Mini's nadir is at +6. If you're able to vary the times, it will help fill in the blank spots on your SS. If you're home, getting a mini-curve (i.e., testing every 3 hours) will also help to sort out when Lantus onset and nadir fall. Likewise, it's important to get at least a before bed test every night.