What’s the max instant current draw from a Li-Ion protected pack?
The overcurrent protection obviously varies with the battery size and its purpose, and the actual threshold value should be defined in manufacturer's specifications. 

If you can't find the actual battery specifications for your particular battery (I admit it is a challenge), you can try to determine that threshold by loading it up with variable resistor at your own risk.

You should consider that usual appliance batteries have a safe discharge rate of about 1C-2C, which, for a 2600 mAh battery would be 2.6A - 5.2A. So the manufacturer would likely set the current limit in accord with the type of cells they are using in their packs. The battery described in this SE EE question has the protection that tripped at about 3 A, causing some problems.

Keep in mind that there are "high-discharge" Li-Ion batteries designed for Radio-Controlled cars and flying apparatuses, they might have the discharge rate of up to 50C or more, or in hundreds of Amps (which is unlikely for the camcorder batteries, but anyway you've been warned).