Though he did include some ejective phonemes, voiceless consonants produced with a contracted glottis, like ch'ah and p'ah, similar to those found in real-world languages like Mayan and Chechen.
But for " ha" you're constricting the air down in your throat at the vocal folds or glottis, and you can't get your tongue down your throat to create that centre blockage.
The different moving parts are known as articulators, and the main ones are the tongue, upper lip, lower lip, upper teeth, alveolar ridge, hard palate, soft palate, uvula, the pharyngeal wall, and the glottis.