```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:
        raise ValueError("Span and rest must be at least 1.")
    if least < 1 or least > span:
        raise ValueError("Least must be between 1 and span, inclusive.")

    stretches = []
    current = start

    while current < end:
        stretch_end = min(current + span, end)
        if stretch_end - current >= least:
            stretches.append((current, stretch_end))
            current = stretch_end + rest
        else:
            break

    return stretches
```