i would also say
a timer issue based on what you have said. if the dishwasher
consistently drains in all prewash and wash phases but will not drain in one of the after rinses that would definately be a timer issue.
your machine has a fill pressure switch that is supposed to keep it from overflowing should it begin a fill period while the tub is already full from the last wash or rinse.
in older machines like the 16 models (i have 3 of em) this switch can become inoperative due to crud build up basically in the small tube that sends water pressure to the switch.
this would result in an overflow if the timer is mal-
functioning. even if you fixed the pressure switch (which is usually an easy fix) your machine still will not drain if the timer is bad.
i don't know if larry has a timer or not, if i remember correctly he told me didn't have kitchenaid timers last time i visited him in cleveland this summer. but i could be wrong, worth a phone call at least.
i don't have any extra timers myself but occasionally i see them on e bay for the older 16 and 17 models that i love to collect.
if all elsae fails you can always run your machine manually using 3 small switches. one to turn off timer motor, one to turn on drain valve, one to turn on fill valve.
most people would not want to go thru the work to hook them up
ot the ordeal of running the machine manually but since i collect them and have a bunch i do have one of my 17 models that i use as a regular machine wired this way. i start it, turn off timer motor motor, fill it, let it wash as long as i want, drain it, and etc. for me it's fun but hey i'm not a normal kitchenaid owner! i use em as a hobby!
but if you can't find a timer and you want to hang on to that machine it can be easily done. or you could add one switch to simply turn on drain valve when timer messes up, that way you could drain it when needed. any questions e mail me!
good luck, hope you find a timer!