So. . .purple dye. . . Are Bees the only efficient option?
Bees are the way to go here. With production upgrades in a gendustry industrial apiary you can get a dye per bee and bee cycle (27.5 seconds).
I'd suggest making red and blue dyes though, as you are more flexible. For the purple wool, you could dye sheep directly, which saves you about 1250 dyes.
Don't be scared of bees. With gendustry, it's quite straightforward. Get Doctoral, Aer, Robust and some of the standard Bees to extract their best features, make a super-bee template and put it on your bees. Put them in industrial apiaries with up to 8 production upgrades and an automation upgrade and they'll generate ressources en masse.
They're also the seemingly fastest way to get diamonds (Diamandi Bees), ender pearls (Winsome bees) and Thaumcraft shards.
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