How to get the texture of commercial ketchup?
Try sugar.  

Per Heinz' website, the ingredients in their ketchup are: 


  TOMATO CONCENTRATE FROM RED RIPE TOMATOES, DISTILLED VINEGAR, HIGH FRUCTOSE CORN SYRUP, CORN SYRUP, SALT, SPICE, ONION POWDER, NATURAL FLAVORING


I notice that they do not include xanthan gum at all, but they do include sugar in the form of various corn syrups.  Cooking plain sugar can can harden it (think the ball stages of candy-making).  I think that what happens in commercial ketchup is not so much a "thickening" as a "hardening" of the tomato syrup, for lack of a better word.  It is likely that during the reducing stage of ketchup making, the sugar reaches what would be at least soft-ball stage if the ratio of sugar to everything else was correct, thus leading to a ketchup that is "thick" but not hard or mucus-y.

Edited to add:  As noted in the comments by @Ecnerwal, Heinz also seems to be using a tomato concentrate, which would include the flesh of the tomatoes.  When I initially read the question, I seem to have missed that you're straining out the solids.  Try leaving them in as you reduce-- the addition of solid matter will also help thicken while providing a better mouthfeel.