Hall:

Grande = caudatum x longifolium
Sedenii = longifolium x schlimii
Schroderae = caudatum x Sedenii

Three sections involved, Section Phragmipedium (Phrag. caudatum), Section Platypetalum (Phrag. longifolium) and section micropethalum (Phrag, schlimii).
All of them grow as terrestrial or lithophytes associated with moss. Some (longifolium) grow at the edges of streams were sometimes they get covered in water.
My experience is: bright light, no direct sunlight; loose media; diluted fertilizer (1/2 strenght) every 2-3 months, never dry out media (moist but not soggy), all my plants are on shallow plates with water CONSTANTLY, some kind of calcium supplement (I steal my mother the thing they use for birds). Hope it helps.
Jose