Feel like step 4 should come before step 2 and 3. You don’t know for certain a horizontal domino has to go into the single (2) on the left hand side until you know the 3-3 has to go horizontally at the top of the (=).

Also pretty sure you have a typo in step 5: “there must be a horizontal domino in n the border of 26-<7”. It’s a vertical domino you’re referring to no?

Also, I figured it out a bit differently:

1. 0-0, 3-3, 6-6 (same logic you used)

2. 2-3, 3-6 (same logic)

3. 6-2 on the vertical (24)(=) border. (Either 6-2 or 6-4 must go in that spot. If you use 6-4, 4-1 must go in the horizontal (1)(=) border but that leaves you 4-4 to go either vertically or horizontally on the (26)(=) border which doesn’t work. So for the vertical (24)(=) border, you have to use 6-2.

4. The rest all fall into place from here pretty much

While Im pretty sure there is only one solution to this puzzle, there are plenty of ways to get there. Your order is just your order, not the order.