You can get that level of support for a minimum of $100 or 10% of your bill on AWS. Their support is excellent. You could always pay for a dedicated host with AWS and reserved pricing.
Is this really true? I've never had this experience with paid AWS support, even spending a lot more than $100/mo (although not as much as Lyft).
Rackspace support ca. 2004 was really fanatical. Like you could call them and get an engineer on the line, working on e.g. your RAID card, in minutes. Without going through a ticketing system or other intermediaries. Some of this was no doubt due to them being a smaller company, but "Fanatical Support" was not just marketing hype.