A simple idea, it would work the same way as silk farming. Itsy Bitsy spider would be male or female, and last around 48 hours. Females would lay eggs only when a male is present (spider eggs slight better Q than parents). Those would hatch into new spiders, taking 16 hours to hatch and 24 hours to mature (feeding period).
Glass box: glass, board and bone glue (sotfcaps spider Q)
Feeding: ants
When quality of ants (food) is lower than of spiders, spider's quality drops. Ant queen will yield a 1.5 bonus to it's Q, and ant empress a 3.5 bonus.
Why do all this? Whenever a spider dies, it has a 10% chance of leaving an itsy bitsy web of the same quality. I assume the webs wouldn't reach qualities much higher than 90, so it is kinda balanced.