The NYT has an excellent overview of the 3-1-1 experience.
It mentions a trick I’ve found to be very effective with getting my bagged liquids past arbirtray and rule-ignorant screeners:
‘Not wanting to have her toiletries tossed out, she assembled some generic three-ounce containers and assiduously spent time pasting manufacturers’ labels on them.
“It was a little insane, but still, I couldn’t believe how the labels stuck,” she said. “If you looked closely you could tell the labels weren’t exactly straight and there was missing information. But I thought, like, who’s going to know from a label anyway?”
Nobody. Actually, despite what a few uninformed checkpoint screeners might say, there is no requirement that a container carry a manufacturer’s label.’
Actually, I just refill containers with similarly-colored liquids - like clear hand soap (for laundry) in empty two-ounce hand sanitizer bottles.