You can get some amazing rack mounted machines now, ok not for cheap, but for relatively cheap given the value that they bring. I'm buying an analytics "box" at the moment with 20k gpu cores, 386GB ram and a 45k iops ssd, ok its $40k but shared across 20 engineers the productivity boost more than costs in really fast. It sounds to me that you need to take an investment case to your boss.
Or if it's just the occasional batch job, use AWS EC2 spot instances. A machine with 122 GB of RAM can often be had for $0.25-0.50 pr hour and sometimes for a lot less.
