If the problems were all server side then you generally wouldn't expect to see this phenomenon where some users are completely unaffected, and others are plagued by constant issues. The resolution might be on the server side, but there's probably an aspect of end user connections that's initiating the problem, and it would be interesting to know what it is.
The DMZ will fix any issues with ports (in case your router's UPnP implementation is struggling with Hitman) so that should be your first order of business: it's just a worthwhile step in general for a console.
The pingtest.net results are the most important ones for gaming so let us know what results you get. In addition to latency it'll let you know how many packets are getting dropped on your connection, and what the jitter is.