I am using one of these washers:
http://www.summitek.com/cascade.html
and I get the same thing. Seems to take about two weeks in the washer but trays will get that slimy feeling almost overnight. Maybe because the water in the washer is moving more. Anyway, I find that the only solution is to take the whole thing apart and wash every panel with warm soapy water wiping each panel with a cloth and then thoroughly rinsing and after re-assembly, a one hour run of fresh water. The dis-assembly, wash, re-assembly takes less than an hour - it is a real PIA, and I would rather spend that hour many other ways - but in the end it is a small price to pay for the results obtained. I think, anyway......
Tim R