Brokering communication between SaaS vendors?

So, my company has been moving things to the cloud like everyone else, with the strategy being SaaS first and then the rest into AWS. One problem I've been having of late is when one SaaS vendors has a VPN tunnel directly to another SaaS vendor without us in the middle, to pass real-time data etc.

Whenever one vendor's support detects a problem that must be fixed by the other vendor, it falls to me / my team to open tickets with both, and act as the middleman with emails / bridges. There is no apparent interest in direct communication to just *fix* the problem, it all gets channeled through us.

A few weeks ago one vendor detected an issue at 4am, and it took until 1pm to get the other vendor to restart a hung service and get things flowing again. In the post-mortem, everyone agreed it should have been sorted much quicker, but neither vendor had a support process built to facilitate that.

Do any of you see that sort of problem? If so, how do you handle it? It's not like cloud / SaaS services will become *less* common in years to come...