Turns out that it's actually 2-bit and not 1-bit. It uses a combination of the EAR and MIC jacks, and when you output through the MIC jack, it slightly boosts the EAR jack. That gives you 4 possible levels, but they are not evenly balanced.
Yes, both Beeper and Recorder bits are changing, but both to the same value, along with all other bits of port FE due to optimization (instruction CPL to set beeper bit to 1 instead of LD A, 16).