Dealing with ISPs/leased-line provider support

Hi r/networking,

Hopefully this doesn't fall under 'early career advice' and is a reasonable question.

To make a long story short, part of my job role is liaising with our clients' ISPs and leased-line providers during circuit outages, and more often than not I feel like I am getting the run around because I don't know how to put the pressure on these big companies to give us the support we need.

Example (the situation I am currently dealing with):

Leased-line down for 5 days and counting, location has a DIA circuit that WAN connectivity can rely on when MPLS is down so no user impact (yet). Opened ticket with provider (won't say who, one of the biggest providers in NA) requesting they troubleshoot and resolve Was routed to a team of 'escalation engineers/managers' who seem to simply be running out the clock until their shift is over, and handing off to whomever is next in their follow-the-sun model. Worked with customer to escalate issue with their account managers at provider, they were brushed off/re-assured that the issue is being worked on just as I was when I escalated to them.

My question is, how would you handle this differently? What would you do to escalate this/light a fire under them so they are providing adequate support during an outage?

Thanks!