We are using Cloudflare enterprise as well and have a phone number to call, including an SLA for P1 support tickets, which I believe is 2 hours. [0]
Never had any issues with receiving solid support but our account manager has been super good. I will say there's been a lot of turnover after they went public but overall the service has been solid for our use case. (delivering terabytes of peer data and analytics a month)
Have you brought any of these issues or concerns up to your account manager? Curious if they had any ways to help.