I haven't tried a dishwasher, don't think I would consider it either. All that yuck going with stuff you eat off or with.
What I do is scrub as much as you can off under hot running water with a wire brush. Then in a small bucket with hot soapy water, soak the mech/tensioner over night. Next day rinse properly, dry wipe. (Optionally leave to dry for a couple of hours.) Re-lube the hinge and pulleys with some decent chain oil. Put back on the bike. I usually do that routine every six months, if it get particularly bad. Kind of like how it is right now. I go to my local hand car wash, bung the chap a couple of quid and he jet blasts the tensioner, hubs and spokes for me. This usually results in cleaning the chain, meaning it will squeek, ride it home which is like 200m. Then wipe the chain down to dry it properly, then re-apply some chain lube on the chain and mech.