The subject line point is underrated. “Reminder” is easy to ignore; “Invoice #[X] for [amount] due [date]” is harder to misunderstand.
I’d also avoid vague body copy like “just checking in.” A stronger reminder usually has four pieces:
1. invoice number / project
2. amount due
3. original due date
4. one clear ask, like “Could you confirm when payment will be made?”
It can still be polite, but it should not require the client to infer what you need.