Amplified computer speakers can be a curse. Not only do they tend to rectify every radio signal for miles around, their wall wart power supplies tend to be horrendous broadband QRM generators. And since things that radiate are usually wide open to RF, the wall warts are sometimes the whole issue. If you have a power line filter handy, I'd try isolating the wall wart on it, and see if that helps.
At lower HF, you need some real inductance to block RF, and it can be hard to achieve with the snap on ferrites. Be sure that the ferrite material you are using works well at the frequency you're having the most trouble with. The 'mix' used in the ferrite can make a big difference. http://www.k0bg.com/beads.html Type 43 beads are useful mostly above 15 MHz.. Type 31 works well at lower frequencies.
I think before investing a fortune in the proper beads, I'd consider moving or changing the feed on the antenna. End feeding the Zepp could be creating an imbalance on your feedline, and undesirable feedline radiation, increasing the RF field where it's not wanted - like in your neighbor's house.
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