```python
from typing import List

def steer_forklift(aisles: int, bays: int, moves: List[str]) -> List[int]:
    if aisles <= 0 or bays <= 0:
        raise ValueError("Both aisles and bays must be positive integers.")

    if not all(move in ["north", "south", "east", "west"] for move in moves):
        raise ValueError("Invalid move word.")

    for move in moves:
        if move == "north":
            bays += 1
        elif move == "south":
            bays -= 1
        elif move == "east":
            aisles += 1
        elif move == "west":
            aisles -= 1

        if aisles < 0 or bays < 0:
            raise ValueError("Forklift would carry the forklift off the floor.")
        if aisles > aisles_max:
            raise ValueError("Forklift would carry the forklift off the floor.")
        if bays > bays_max:
            raise ValueError("Forklift would carry the forklift off the floor.")

    return [aisles, bays]
```