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I normally make the roux the day before and put it in the fridge overnight, so it's one less thing to deal with when I'm making the rest. It obviously does harden, but I take a ladle of the liquid from the main curry pot, use it to moisten the roux block in a small bowl or pot until it becomes a paste, then add that paste to the main pot.
The way I've always made Japanese curry was to start with sauteing the onions in the pot, then add the chicken and let it brown, then pour in the stock and add the other ingredients (carrot, potato, etc) at as needed for their various cooking times, and then finally once it had simmered until the vegetables were cooked I'd mix in the roux. I'm not even sure how you'd have to change things if the roux was in there earlier.