Could I get some informed guesses on a situation?

The patient is a Sears-rebranded Whirpool of about 5 years vintage. Pretty
standard - conforms to a number of Whirlpool diagrams I see on the web. A
circular finely-screened cover under the lower pump arm is held on via 8 Torx
screws, and upon being removed shows the rotating pump.

The unit suddenly stopped draining. On a drain cycle, there's lackluster pump
action for a while, and then just a spurt of water every second or so. The
result is that about half the water is pumped out, and half still remains in
the unit.

The hose between pump and airgap is clear.

Upon removing the hose, and starting the fill cycle, water immediately drains
through the pump drain port via gravity.

On the drain cycle, there's evidence that water is being pumped through the
spray arms rather than (totally) through the drain port, because concave
utensils on the top rack fill with water even after being manually emptied as
an experiment.

Could this be the mythical check valve? I would think that valve would sit
between the drain port and the hose to prevent/cause water go go through the
port rather than through the spray arms, but obviously I'm mistaken. Where is
this check valve, and how does it do its thing?

Advice eagerly solicited - after two days of pumping out the unit with my
Rainbow vac, it's getting to be annoying!

Art