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The easiest thing in the end might be to just bite the bullet and build a faster storage network. But you already said that you don't want to do that.
If you can monitor your virtual environment in real time, you can see the way you storage I/O is being consumed. You should be able to identify which VMs are using up your resources, as well as identify the hosts that have excess capacity available. This should allow you to shift your VMs around to better distribute the load during those peak events and minimize the performance degradation that you are experiencing.