If you are finding the noise during the wash cycle, then the wash motor is the likely problem. They are lets say low cost so it doesn't take much more than a plate chip to begin causing problems. The motor is easy to replace by pulling the dishwasher from the cabinet and laying it on it's back. Two screws and a wire harness is all there is to it. As for the insulation, I would suggest an insulating blanket from another model (like this one AP3875489) then just do any minor adjustments you need. This way you are using something that was designed for the purpose you are looking for and you know it will work.

The motor comes with everything you will need. As for drying, without the use of rinse aid in the dispenser, the dishes will never fully dry. A 3 hour cycle is not unheard of anymore in dishwashers, and yes, the better quality for the extra money is usually missed if you step down.

The blankets are not all the same, but close enough for getting stuck between the cabinet and the tub, and yes I would put whatever you want to reduce noise. Much of what you hear is not from the tub, but the motor noise bouncing off the flooring, so some insulation down behind the kick plate would work well too. Just don't put it down in such a way that it becomes a sponge if the unit ever leaks. Thats the kind of thing you want to know asap. And it sounds like you have already figured out the new way dishwasher work. It is difficult to explain to people when their old DW worked great, but they wanted to update the kitchen that now the DW'ers are energy efficient and conserve water so now you need to change the way you use them. The newest Whirlpool units can run for 4+ hours and that is considered normal.

My best advice is to run the water hot at the tap before starting a load, and limit adding plastic and wood items to normal glass and dish loads as their lack of thermal mass doesn't allow them to shed water like everything else. And the addition of an insulating blanket will allow the tub to retain more heat and thus, better drying of the dishes.

I'll be here.