I agree though, in my experience it seems like status pages don't always accurately indicate downtime. Third party status pages might be more reliable.
Your aggregator looks really useful, bookmarking it.
I would suggest having your primary account maintainer and procurement department check the language in your contract. If it does not exist, then have them amend the contract with language that requires the status page to be accurate and that allows you to monitor them from multiple locations. Perhaps consider adding language that allows you to share your monitoring results with them, your internal and external customers.
I am not a lawyer and I do not play one on TV. This is not legal or medical advise. Do not stare at happy fun ball.