If it cannot be moved
The south belongs to Yama and carries weight; the tradition does not place worship here. If the room is fixed, seat the worshipper facing east or north so the direction faced corrects the direction sat in.
What the ದಕ್ಷಿಣ governs
South is Yama’s direction, and it carries weight rather than light. The tradition builds it up — heavy walls, storage, mass — and keeps openings modest.
Where the ಪೂಜಾ ಕಕ್ಷ belongs
The pooja room belongs to the light half of the plan. The tradition puts it where the first sun falls and keeps it away from anything heavy, wet or waste-carrying — including sharing a wall with a bathroom, which matters more than the compass point.