Your debugging was only rudimentary.
Use at least "!analyze -v" to get some more information out of the dump.
From what we have so far, q57xp32.sys is the only hint, that is true.
But there may be more info as to the process context in which the driver fails. And its also very interesting to look at the call stack (commands "kb" or "kv").
If it turns out that there is no other candidate to blame than q57xp32.sys, then running the current HP driver doesn't help because it could be buggy and in need of fixing. It could also conflict with some other driver/process specific to your server setup. In which case it might be safer to revert to an older version of the driver that however is confirmed to work.