OK, my head was "in and locked" when I asked "Where is the fuel going?" With the primer in and locked, there is no fuel in it. Duh. So yesterday I capped off the outlet and slowly pulled out the plunger. There was a lot of resistance, but it would suck fuel into the chamber. The plunger wouldn't go back in, though, as it shouldn't. This told me that 1. The inlet check valve was allowing fuel to enter, but not to go back up into the tank. 2. The internal O-rings weren't leaking past.
Just to be sure, I removed the plunger, and inspected and lubed the O-rings (with DC-4) anyway.
After removing the outlet cap and restoring the system back to normal, I pumped the primer again and got the same old thing: I had to pump it 4 times before there was any resistance on the plunger in either direction. The only thing my (alleged) brain can come up with is that retracting the plunger is sucking air into the chamber through the outlet.
I had thought that would mean the outlet ball check valve was bad until I realized that the ball itself is on the end of the plunger, so when you unlock the primer, there is no check valve. The ball is on the end of a spring-loaded rod which is connected to the plunger. This must be why you're supposed to check "primer in and locked" if your engine is running rough. Another "Duh" moment...
That being the case, how does pulling the plunger out manage to suck fuel from the tank when it can just as easily suck air/fuel from the primer line? All I can think of is that this design depends on the resistance of the small orifice at the primer fitting in the cylinder. I know that there's resistance there because when the primer chamber is full of fuel and I push on the plunger, it goes in slowly as the fuel is injected into the intake.
Which brings up another question. My primer line is probably 50" long in total from the panel to the #1 cylinder. With the engine running, does the vacuum in the intake vaporize the fuel in the primer line so that it's basically empty the next time I go to start up? That would explain the 3-4 pumps required to prime the primer. I guess I could check the next time the cowling is off, but I already feel like I'm over-thinking this.
It's really embarrassing that I'm having trouble understanding how this supposedly simple system is supposed to work.