I mixed the dry spice mix together before chopping the onion and garlic. Then I cubed the beef so that each piece was about 1/2 the size of those used in the previous batch, Each cube was about 3/4 of an inch on a side.
I heated up 3 Tablespoons of olive oil on the kitchen stove in a 2-1/2 quart stainless steel saucepan and added the onion and garlic. After the onions had begun to clear, I added the cubed beef and browned each piece on all sides. I added the dry spice all at once and stirred to coat all of the meat. I immediately added the tomato sauce and water and brought the mixture to a simmer.
While the chili was cooking, I tasted it periodically, but I had a hard time telling whether any adjustments were needed. Overall, I made much fewer adjustments this time around compared to last time. I did add 1/2 teaspoon of salt and 2 teaspoons of sugar after about an hour and a half.
Other than that, I just skimmed the fat after a while. I tried turning the burner off to make the skimming easier, but ironically I had a much harder time with the burner turned off. The fat just didn't seem to want to stay on top long enough for me to get it. I turned the burner back on and tried again. I was able to remove a lot more fat while the chili was simmering compared to when it wasn't. I used a small ladle for this task.
I added the lime juice about 15 minuted before the end of cooking. The overall cooking time was about 2 and 1/2 hours. The taste of the Chipotle pepper was noticeable at first, but faded as the chili cooked. I decided not to adjust that though.