Hey, Tony. Thanks for the response.
At startup, both variables are #$00 up until the point in which my custom code assigns them to be #$00 just before the title screen displays. They then remain #$00 until just after the players are selected.
At this point, $FFF0BE increments to #$01. Then $FFF0BF does the same. The process repeats, yielding a value of #$02 in both $FFF0BE and $FFF0BF. The Stage 1 Start tiles display, and the game starts. Player 1 receives one health point. Player 2 receives the standard full life bar.
EDIT: I think your suggestion may have done the trick. If the increments duplicate in sequence, I might need to change the player 2 comparison to #$02 rather than #$01. Gonna give that edit a shot and see.
EDIT 2: There's one more nuance here, where some CMP/BEQs need to be considered in situations where there's a second player versus where there isn't. I'm cleaning up the custom code a bit, and will stick it in my blog in the Personal Projects forum for those interested.