Hmmm.... OK. Let's just follow that thought. --
So I think aphids are superbly adaptable, and since they bear live young, even if the pepper sap could be toxic, just a very few that survive could produce several generations in a short time that would be genetically tolerant or immune. The ones that are still on your plants could all have adapted, while the newly purchased ladybugs don't have that tolerance. (IF you could somehow get them to survive and produce several generations feeding on scorpion immune aphids, maybe you could end up with resistant/immune ladybugs...?)
Whatever -- if you only option is to eradicate the aphids yourself, I think what I would do is start by putting the plants in a rest/near dormant state by withholding water and putting them in cooler temperature and dimmer light until the leaves start to yellow, then I would drastically prune them and defoliate them until you are only left with scaffolding/framework structure of strong branches, which would be much easier to treat with regular application of organic aphid killer like insecticidal soap or neem oil solution or spinosad. If you have two isolated areas to grow them, you could do this with just one plant as a trial.
Then after you are sure all the aphids have perished, you can bring the plant back to light and warmth to grow new leaves in a protected setting so they won't be re-infested (keep an eye out for ants that might bring new aphids from their colony stock. ) This is the tough part -- because the new peppers buds and flowerbuds are vulnerable -- you might want to get another batch of ladybugs at this point if you see aphids... OR do my bamboo skewer dipped in soapy water trick to pluck off the aphids.... OR just keep up with the weekly spray treatment.
BTW, not sure if you need to change out the soil each time -- repotting could be stressing them which would make them susceptible to pest infestation.
P.S. FWIW -- My Indoor Garden Patrol ladybugs have been protecting the Bhut Jolokia and Scotch Bonnet peppers. I have a Golden Habanero, too. Not sure if they are in any way comparable.
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