I assume your "speakers" have a preamp, amplifier, and possibly a mixer built-in? I think you are missing the preamp.
With "MP3" speakers (I assume these are speakers that plug into an MP3 player or computer) you don't have the preamp. The signal out of an MP3 player or computer is about 100 times the voltage you get out of a microphone.
The least expensive solution (without building something yourself) would be a small mixer something like this
. Just make sure you buy one with a microphone input.
...as far as I can tell, are electret mics, but they draw power from the speaker when someone plugs one in.
That would be unusual. Electret (and condenser mics in general) do
requiere power. Dynamic mics don't need power. Computer mics are unique. They run on 5V supplied by the soundcard. I don't know of any preamps, mixers, or PA systems that work with computer mics. Studio condensers (with XLR connectors) run from 48V "phantom" power, supplied by the preamp, interface, or mixer. Stage/performance condensers (with XLR connectors) usually have a built-in battery, and sometimes they optionally run from phantom power.