Use a blender. This will give the sauce more body without having to cook it to death. Blend very well then taste for texture. If needed (this will depend largely on the cherries), force through a strainer after blending.
The proportions look good. I think I'd increase both chilies though, upping the ancho to 2-3 t and the cascabel to 3/4-1 t. Consider as a starting point halving both the sugar and the drippings. Start with 2 T each, then scale up, tasting as you go. You might very well end up with the levels you predict, but both of these elements have a significant impact and I think it's worth being deliberate with each.
Yes, add thyme. I'd suggest 1/2 t. I'd also suggest a pinch (1/16 t) of ground clove.
Yes, Worcestershire, and your thought of 2 t sounds right. I'm also thinking a little cider vinegar for its acidity and fruity notes (I like unfiltered cider vin for its fuller flavor--TJ's has a good one--but use whatever you have).
If I might suggest a procedural flow...
Chop the onion*, mince or press the garlic; reserve the garlic separately.
Melt the butter and when the foam subsides add the onion. While the onion softens, measure and mix in a small bowl the cumin (use ground), both chilies, the cinnamon, black pepper and ground cloves; reserve. Measure the thyme; reserve. Measure the celery; reserve. Have your bottle of cider vin ready and the tomato can opened. Measure the cherries; reserve.
When the onions are translucent stir in the thyme. Take the onions to the point where they are just starting to brown in spots. Crank the heat to high then immediately add the garlic and the contents of the little bowl of mixed spices. Cook, stirring constantly, till the garlic is very fragrant and the spices' aromas bloom, about 45-60 secs. Immediately add a good splash (about 2 T) of cider vin and the cherries. Quickly tip the pot toward you so that the liquid collects and you can eyeball the quantity. Simmer strongly to reduce the liquid in the pot to about 1/3 its original volume (tip the pot again to compare with what you saw originally).
Add the tomatoes and their juices, the celery seed, the Worce and a little salt. Bring just to a boil, stir in 2 T each of the sugar and drippings, cover, reduce the heat to med-low, then cook till the cherries have completely softened and the flavors have blended.
Puree the sauce in a blender, check texture (forcing through a sieve if necessary), then return the sauce to the pot. Bring just to a simmer. Adjust thickness by reducing the sauce gently, if desired. Adjust sugar and drippings, add 1/2 T more of each at a time and stirring to be sure the sugar melts and mixes in before tasting again.
* Not required, but a 1/4 c of finely chopped red bell pepper is a thought. Add to the pot with the onions.