"I see several DW with the top door vent, and some that don't seem to have any. Do those vent steam? And if so, from where?"

The vent of the KitchenAid KDTM604KPS appears to be at the bottom of the door. You can see this if you look at part #18 ("duct vent") on the CONTROL PANEL AND INNER DOOR PARTS diagram on SearsPartsDirect.com (https://www.searspartsdirect.com/model/jwyt9llpl7-000593/kitchenaid-kdtm604kps0-dishwasher-parts).

Thank you @wdccruise, I didn't think to check the parts diagrams! I am now considering the Bosch, my husband wants the 500 with AirDry, but I'm wondering how much steam escapes when the door pops open. Though maybe it escapes all at once, and so condensation isn't an issue. I'd prefer the 800, but the exploded view doesn't give me any indication of where the duct fits in the overall scheme. I'm assuming the door, and from the shape figure it probably vents at the bottom somewhere as well.

I have an old Whirlpool Quiet Partner 1 with a top front vent (https://kithzentoolz.blogspot.com/2020/04/whirlpool-quiet-partner-1-dishwasher.html). A tiny amount of moisture is emitted through the vent while the machine is operating but no water runs down the door. I open the door to dry the dishes; moisture dissipates within a few seconds.

Are you sure you need a new dishwasher? Mine stopped mid-cycle and I spent weeks trying to figure out why. It turned out that a non-obvious fuse needed to be replaced. Total cost: $9.

Yes, it's the control board in ours. We replaced it once already after only two years of use, and it's stopped again exactly two years later. They are expensive, and at this rate, I expect it to fail again in two years if replaced, so we just want a better dishwasher. This was a low-end model GE that was bought as part of a package when we first moved in and there were no appliances in the house at all.

The reason we have trouble with dripping is because the steam is so hot, and the quartz countertop is so cold. A laminate countertop with a moisture barrier would probably be fine.

I thought it was my control board. It turned out to be the fuse which was embedded in a plastic part attached to the control board, not the control board itself.

"The reason we have trouble with dripping is because the steam is so hot..."

Have you checked your household water temperature? It should be 120 degrees.