How to implement overload of `__setitem__` for `MutableSequence`?

I'm trying to implement my own MutableSequence but struggling with the proper way to implement the @overload

Here's my code example:

from typing import Iterable
from typing import List
from typing import MutableSequence
from typing import Union
from typing import overload


class RecordBehaviourList(MutableSequence[str]):
    def __init__(self, lst: List[str]) -> None:
        self._lst = lst

    @overload
    def __getitem__(self, index: int) -> str:
        ...

    @overload  # noqa: F811  # TODO: flake8 3.8
    def __getitem__(self, index: slice) -> MutableSequence[str]:
        ...

    def __getitem__(  # noqa: F811  # TODO: flake8 3.8
            self,
            index: Union[int, slice],
    ) -> Union[str, MutableSequence[str]]:
        return self._lst[index]

    @overload
    def __setitem__(self, index: int, value: str) -> None:
        ...

    @overload  # noqa: F811  # TODO: flake8 3.8
    def __setitem__(self, index: slice, value: Iterable[str]) -> None:
        ...

    def __setitem__(  # noqa: F811  # TODO: flake8 3.8
            self,
            index: Union[int, slice],
            value: Union[str, Iterable[str]],
    ) -> None:
        self._lst[index] = value

    def __delitem__(self, index: Union[int, slice]) -> None:
        del self._lst[index]

    def insert(self, index: int, value: str) -> None:
        self._lst.insert(index, value)

I've taken the overload definitions from this example (?) but perhaps I'm doing this incorrectly?

For now I can # type: ignore but seems non-ideal

Here's my version information and current output

$ mypy --version
mypy 0.740
$ mypy t3.py
t3.py:39: error: Invalid index type "Union[int, slice]" for "List[str]"; expected type "int"
t3.py:39: error: Incompatible types in assignment (expression has type "Union[str, Iterable[str]]", target has type "str")
Found 2 errors in 1 file (checked 1 source file)

まず、mypy 0.740 を使って t3.py の例を再現し、typeshed からリンクされている overload 定義と比較します。List[str] に対する setitem の実装が拒否される理由を調査します。正しくサポートされる型付けを確立するか、mypy の診断上の問題を確認できれば完了です。