This is almost certainly not the IO scheduler's problem. IO scheduling priorities are orthogonal to CPU scheduling priorities.
What you are likely running into is the dirty_ratio limits. In Linux, there is a memory threshold for "dirty memory" (memory that is destined to be written out to disk), that once crossed, will cause symptoms like you've described. The dirty_ratio values can be tuned via
When the threshold is crossed, in an attempt to "slow down the dirtiers", the Linux kernel will penalized (in rate-limited fashion) any and every task on the system that tries to allocate a page. This allocation may be in response to userland needing a new page, but it can also occur if the kernel is allocating memory for internal data structures in response to a system call the process did. When this happens, the kernel will force that allocating thread (again, rate-limited) to take part in the flushing process, under the (misguided) assumption that whoever is allocating a lot of memory is the same thread that is dirtying a lot of memory.
There are a couple ways to work around this problem (which is very typical when copying large amounts of data). For one, the copying process can be fixed to rate limit itself, and to synchronously flush data at some reasonable interval. Another way that a system administrator can manage this sort of task (if automated of course) is to use Linux's support for memory controllers which essentially isolates the memory subsystem performance between tasks. Unfortunately, it's support is still incomplete and I don't know of any popular distributions that automate this cgroup subsystem's use.
Either way, it is very unlikely to be the IO scheduler.