The last two years Ive brought my pepper plants into the house from outside Ive had issues with aphids. I tried alcohol, soap, blasting them with the hose outside daily, asking them to leave without any luck. I tried some aphid incecticide and all it managed to do was make my house reek of fish oil. I even was seriously considering letting lose a colony of lady bugs inside my house but realized I was being ridiculous. Both years ended in my tossing my pepper plants. Good luck.
I played with the Kratky method with herbs, and I had issues with algae once I introduced nutrients. I knew it would probably happen, and I warped the mason jars in painters tape, fully aware that the tape wouldnt do the best job at blocking out the light, but I didnt feel like painting them black. Im skeptical this method is all that viable for keeping plants like peppers long term, so it didnt really appeal to me for pepper plants. I will say though, as someone who for the longest time was against the hassle of hydroponics, after seeing the results of the Kratky method with basil, its definitely changed the way I view hydroponics, and Im now in the process of building an aeroponic system, but my intention is not to grow fruit with this setup, but to instead use it primarily to keep mother plants to clone my pepper army.
I think the Kratky method is probably a pretty good method of propagating clones, but I think an aeroponic bucket would work even better, and be a lot easier to maintain.