I tried changing the Speed by Icon Icon Animation parameter to sync to Particle Age. I get the same result. When I animate the emitter size, the width of the particle stream changes, but it does so from the emitter outward. I want the stream to narrow at the bottleneck (and later enlarge again if necessary), not at the emitter.
I did come up with a sort of solution, but I'd like to make this work by animating the emitter if possible. The solution was to shoot the particles into a tube of varying width and make the tube a deflector with a UDeflector. The particles bounce off the walls and narrow down. This could work, but I'd like to be able to animate the width of the stream from the emitter if that's possible.