Western Kingbird was eliminated because of the thick bill, darker gray coloration, brown tail and lack of white edging, and ultimately vocalizations. A comparison shot with both Tropical and Western Kingbirds in the same frame were obtained later.
Cassin's Kingbird was eliminated because of the thick bill, yellow/green breast, and vocalizations.
Thick-billed Kingbird was eliminated because of the lack of a black cap, less white in the throat, smaller bill, and black wings.
Couch's Kingbird looks identical to Tropical and can apparently only be identified without hesitation in the hand. The vocalizations clinched the ID of Tropical.
We learned later that the vocalizations we heard are called by Nathan Pieplow as Chitter calls.