This seems like a tasty recipe for chicken, but it doesn't strike me as a carne asada (would that be pollo asada?) type of flavor.
For the marinade itself, you might try adding any or all: fresh garlic; cilantro or coriander (same plant, former is leaves; latter is seeds – will have different results in flavor impact, see which or both you like best); chipotle peppers; paprika; oregano.
I also like to use more than one citrus in mine, usually either lemon and lime, or lemon, lime and orange juices. Always fresh-squeezed; if they just aren't available now where you live it's worth waiting until they are.
Some oil added to the marinade would help the marinating process and deepen the flavor. For beef, I'd use peanut oil; for chicken, maybe grape seed or avocado. You could go with EVOO if you're attached to it, but it seems the strong flavors of whatever-meat asada would drown out the subtle notes of a good EVOO.
To punch up the umami you could add some dried porcini mushrooms just before you throw the already marinated chicken into the pan. Either very finely ground and lightly sprinkled over the meat, or reconstituting the mushrooms and using the reduced liquid in the marinade.
Personally, I would prefer grinding the dried ones into a fine powder. This also gives you an opportunity to layer in more flavor by adding any or all to the mushroom pieces in the grinder: garlic crystals, peppercorns, dried chipotle peppers, coriander seeds, smoked paprika, dried ginger.
If at all practical where you live, it will always taste best charcoal-grilled, even worth huddling in the freezing cold of winter to tend the barbecue.
And one last note, you can never go wrong using fresh, whole seed forms of your spices, lightly toasting, then grinding them just before use. They keep a lot longer than the powdered versions too, so it's a worthy investment even on a tight budget if you're able to pick up a new one or two here and there.