Apparently you've discovered already that mainframes are good at writing large numbers of large files. They're good at reading them too. But that aside...
IBM has been pushing hard on Spark on z/OS recently. It's available for free, although if you want support, you have to pay for that. See: https://www-03.ibm.com/systems/z/os/zos/apache-spark.html My understanding is that z/OS can be a peer with other machines in a Spark cluster.
The z/OS Spark implementation comes with a piece that can read data directly from all sorts of mainframe sources: sequential, VSAM, DB2, etc. It might allow you to bypass the whole dump process and read the data directly from the source.
Apparently Hadoop is written in Java, so one would expect that it should be able to run on z/OS with little problem. However, watch out for ASCII vs. EBCDIC issues.
On the topic of using Hadoop with z/OS, there's a number of references out there, including a red piece: http://www.redbooks.ibm.com/redpapers/pdfs/redp5142.pdf
You'll note that in there they make mention of using the CO:z toolkit, which I believe is available for free.
However you mention "unfriendly". I'm not sure if that means "I don't understand this environment as it doesn't look like anything I've used before" or it means "the people I'm working with don't want to help me". I'll assume something like the latter since the former is simply a learning opportunity. Unfortunately, you're probably going to have a tough time getting the unfriendly people to get anything new up and running on z/OS.
But in the end, it may be best to try to make friends with those unfriendly z/OS admins as they likely can make your life easier.
Finally, I'm not sure what analytics you're planning on doing with the data. But in some cases it may be easier/better to move the analytics process to the data instead of moving the data to the analytics.