I may be too late, but that is a sizable gap. If you want your unit to be as quiet as possible, I suggest going back to your first thought with a shim piece of wood to be put under the DW, but it should be full sized, not just the back. Truthfully it is a very minor difference, so if you have it setup already, don't worry about it. The general rule is for noisy items you want to keep the legs as short as possible to reduce vibration.

If you can send the drain down through the floor to a lower level P trap, you can do that. My saying this is not a recommendation "per se" in and of itself, it is just information, which may need further caveats. If the P trap for this DW is in the kitchen, you need to install a high loop. If you know what a high loop is, install that. High loop means to raise a portion of the dishwasher's flexible drain line as high as you can under the sink (e.g. with a piece of bailing wire). This will prevent contaminated water from backing into your dishwasher, unless the backup goes right up to the rim of your sink, in which case, an above-sink air-gap is the only thing that will prevent cross-contamination. The DW drain line branches into the sink drain line below the sink -- regardless of what type your faucet is. I suspect you have a contractor who I would consider a case of borderline fraud. Your contractor must know what a high loop is. He also must know that any dishwasher drain connecting to the kitchen P trap goes first through a high loop or an air gap. In both cases (high loop and air gap), the drain plumbing connection has no relationship to the faucet you chose to install. That is supply plumbing not waste plumbing. Perhaps I have misunderstood your post or you have misunderstood what you thought he said, or some other explanation is possible, et cetera. If not, you have a special case of a contractor saying that the faucet prevented him from raising the dishwasher hose in a high loop and thereby routing its waste water up first before it goes down into the P-trap and the house drain. HTH David

IMO, no people install hidden control exposed when the door is closes (hence hidden control). Preferably, the door should flush with the rest of the cabinet if the depth of the opening allows. Your model should have other means to show the status of the DW, such as projecting colored light and/or remaining time on the floor, etc. You are free to open the door when the DW is working to check additional status information and/or change settings/programs. Actually the control and/or display may not even work when the door is closed as they are supposed to be hidden. The gasket you mentioned should kinda be bent or compressed against the sides of the DW opening so that noise or moisture is somewhat blocked.

Workers do strange things around construction sites. Manys a time I've removed nails and trash from inside dishwasher. I once was walking through a new home with developer's sales lady when she picked up a few bits of trash and threw them in the washer.. From then on when I installed dishwashers in new construction,I disabled switch at door latch so noone could start machine between install and when I returned to do final set up for owner. You must pull machine a few inches from beneath counter top to look at door switch. I generally pulled one wire and taped it. It's also possible latch isn't properly adjusted to close switch when latch closes.