This has happened before with Intl Outdoor blue, their overcurrent protection was set at 3A 
and caused all sorts of trouble. They changed it to Black version with much higher current trip protection.
https://budgetlightforum.com/t/-/5657
You could, with proper care, remove protection circuit from one battery to confirm. If that battery runs without problem at full charge, then this theory is proven.
As for protection circuit, you seem to be:
1. Charging with a good well-known charger
2. Using original battery from Panasonic (one of the safest)
3. Running single battery lights only
So IMO you're ok to use unprotected battery.