I sweat gallons too. Any sweat band or sweat cap is going to do nothing for you if it becomes saturated and the wind is not streaming the resulting excess away from your eyes.
I had some problems recently with the sweatVac that I've used for years. I found out that I needed to insure that it was pulled down to just above my eyebrows and have some exposed to the wind. Perhaps that helps evaporate the sweat quicker on the part that's not covered by a helmet.
I wouldn't expect it to do very much for any sweat containment when just walking or milling about. Airflow and evaporation are one of the things it and others need. Perhaps another helmet promoting airflow while biking will help. But for standing, you need a thick sweat band that you can ring out often.
Also, if the sweat is stinging your eyes quite a bit, then you might have some other minor issues going on and might mention it next time you are at your eye doctor for a checkup.