Took a look at the housing situation across Primal (checked late night April 27th/early morning April 28th EST):

Leviathan:
Goblet- 2 smalls
Mist- 2 smalls
LB- Nothing available
Shirogane- Nothing available

Behemoth:
Goblet- 1 small
Mist- 2 smalls
LB- 2 smalls
Shirogane- Nothing available

Excalibur:
Goblet- 1 small
Mist- 2 smalls
LB- 2 smalls
Shirogane- Nothing available

Exodus:
Goblet- 4 smalls
Mist- 2 smalls
LB- Nothing available
Shirogane- Nothing available

Famfrit:
Goblet- Nothing available
Mist- 2 smalls
LB- 1 small
Shirogane- 1 small

Hyperion:
Goblet- 4 smalls
Mist- 1 small
LB- Nothing available
Shirogane- Nothing available

Lamia:
Goblet- 6 smalls
Mist- 1 small
LB- Nothing available
Shirogane- 1 small

Ultros:
Goblet- 2 smalls
Mist- 1 small
LB- Nothing available
Shirogane- Nothing available