Your first question answered! And then some!
No dishwasher produced in this country allows for cold water inlet supply. If you read your installation manual, you will see it tells you it needs water of at least 120 degrees and goes thru that whole "run the water in the sink first" to get it as hot as possible to cut down cycle times. But they never consider that in a situation like yours and even mine here in Fla, with the pipes under the slab, the water cools down so much between the cycles on these machines that heat and pump until the set temp is reached, that the next fill and subsequent ones are usually with cool water and not hot.
I had no problem when I had my KDS18 as a daily driver because it had relatively short prewashes and the main full cycle was was like 8 minutes and then the 3 after rinses or short duration. by then, the water was pretty hot and the sani cycle heat time was not excessive.
But to answer your question, you MUST use HOT water to supply the machine.
The alternative suggested about the instant hot water heater is a good one if you can locate it as close to the d/w as possible and you can maybe even back feed the sink and disconnect it from the original house plumbing.
Another possible suggestion for you would be to install a 6 gallon electric unit under a cabinet and turn it on prior to running the dishwasher. You could even supply it with hot water so you have less recovery time. They come wired for 120 or 208/240 volts.
I installed one of the Watts recirculating pumps and 2 regulating valves and they DO work but my electric bill increased because the water coming back to the electric heater made it run longer. I have 2 pilot lites hooked up so I can tell when the elements are heating and within maybe 3-5 minutes of circulating, the bottom one pops on and starts reheating that cooler water.
I used the timer on the unit and it is accurate but a better alternative seems to be a radio controlled adapter that plugs into the outlet and you can then turn the pump on and off, for as long as you need it on. Just as long as you leave the pump in the on position,the remote controls it.
One great thing is the fact that you DO have nearly instant hot water for the shower in our bedroom which is a good 70 feet from the heater.
One last suggestion would be to install multiple instant heaters outside the house near each of your bathrooms and since the pipes run thru the attic, you can grab the hot and cold water supply and isolate each area by installing valves and bypasses. Surely a nice cool weather project.
Enough things for you to worry about?
Oh and make sure you soften that cold water as well.
The salt system is probably the best way to go no matter what as the use of a reverse osmosis system can become problematic especially with copper piping I have been told since it will attack the pipe itself.
If anyone else has info on this phenomenon, please inform us.