Nonexistence conjecture for three odd-rank homogeneous spaces

For an integer $m$, consider the homogeneous spaces

$$\operatorname{SO}(2,2m+1)/\operatorname{SU}(1,m),\qquad \operatorname{SU}(2,2m+1)/\operatorname{Sp}(1,m),\qquad \operatorname{SU}(2,2m+1)/\operatorname{SU}(1,2m+1).$$

Nonexistence conjecture. None of these homogeneous spaces has a tessellation. These are presented as three special cases of Kobayashi's general conjecture; the supplied source gives no resolution status.