```python
def carve_shift(start: int, end: int, span: int, rest: int, least: int) -> list:
    if not all(isinstance(x, int) for x in (start, end, span, rest, least)):
        raise ValueError("All arguments must be whole numbers")
    if start >= end:
        raise ValueError("Start must precede end")
    if span < 1 or rest < 1 or least < 1 or least > span:
        raise ValueError("Invalid span, rest, or least value")
    
    stretches = []
    current_start = start
    
    while current_start < end:
        stretch_end = min(current_start + span, end)
        if stretch_end - current_start >= least:
            stretches.append((current_start, stretch_end))
            current_start = stretch_end + rest
        else:
            break
    
    return stretches
```