A quick Google search on the error he's getting says it's an Apache error either from invalid file permissions or running out of memory. His provider refuses to transparently increase memory so the hypothesis seems stronger here. Now just test it by spinning up a simple load balancer, clone your website on a different server, split the traffic 50/50, and see if the errors continue. Repeat this process until you've isolated the issue. Trying to solve the problem by adding a cache layer isn't going to help before the problem is understood.