A 300mW omnidirectional voice transmission heard over a distance of 384,000 km.... truly remarkable!!
Yes, and the truly ironic thing is that had Baysinger tried to receive the signal that was
intended to reach Earth, he would have failed.
The LM had only a single S-band transmitter. It could operate in two modes: PM (phase modulation) and FM (frequency modulation). PM was the normal mission mode. It had a strong carrier component that was used for continuous Doppler velocity tracking, with subcarriers for narrowband FM voice and PCM (digital) telemetry. It could also loop back a ranging signal when enabled. All these signals (except ranging) were narrowband, meaning that the receivers on Earth would not let in a lot of thermal noise, which is proportional to bandwidth. Several hams did successfully receive the Apollo S-band PM transmissions on later flights with backyard dishes.
But PM could not carry wideband video; that's what FM was for. FM has the property that if you go wideband, meaning that you occupy a RF bandwidth considerably wider than the information you're sending, you get a substantial increase in recovered signal-to-noise ratio
provided that your received signal is stronger than a given threshold. Otherwise you get nothing. (This is why FM radio sounds better than AM, but degrades rapidly as the signal weakens.)
Eagle was transmitting FM and video during the EVA, and to get that wideband signal above threshold very large receiving dishes were required (see
The Dish). Anything Baysinger could have built would have gotten nothing at all.
The transmitter in Armstrong's PLSS generated only 300 mW into an omnidirectional antenna, but it was narrowband AM and Baysinger was able to capture it with his homemade antenna. It was by no means strong, but it was definitely there. Had he tried to listen for Aldrin's transmitter (which was intended for Armstrong's relay receiver) he also would have failed because that transmitter used FM, and the signal would have been below Baysinger's receiver threshold. So he did his homework and picked the right problem to solve.