Honestly, dishwashers are amazing. I've rented a bunch of different and when I rented a place without a dishwasher, I thought it'd be no big deal. No way. Dishwasher is so worth it. I refuse to rent a place that doesn't have a dishwasher (and in-suite laundry -- shared laundry is also a pain).
The kind of dishwasher I have might actually be a good fit for you! It's pretty small and on wheels, it hooks up to the sink faucet to run, and it has a countertop that's pretty useful on its own as a moveable kitchen island
No need to scrub them most of the time. Technology Connections's tip of putting some detergent outside of the dispenser seems to help a little.
I have one thing that I've found needs to be scrubbed (a cup shaped thing that will have cake on egg), but almost everything else seems to get cleaned perfectly.