Evening,
I have been using EVA's with VMware and Linux VM's for a long time and had great success. A few items to consider:
- Round Robin is supported on AULA arrays like the P6000 as long as you are running 4.0 or above but make sure you have it configured correctly. If not it could really be thrashing the disk a good review is here with settings: http://www.vmware.com/files/pdf/techpaper/hp-enterprise-virtual-array-family-vsphere-configuration.pdf
-Linux going read only 94% of the time in vmware is caused by loss access to backend storage longer than your linux kernel likes it can be only resolved by rebooting or remounting if not root. I rarely seen it happen with I/O busy but it's possible. You should be able to see this type of I/O wait with esxtop (Take a look at this simple article or the vmware ones on it Identify storage performance issues with esxtop | loopbackconnector)
- I cannot comment on the backup because I don't know what type of backup your doing. If it's san based or vmware based or agent based. I suspect it causes a lot of I/O
Another way to address this issue is allow Storage DRS to fix any inbalance in your cluster.
Please let me know if you have additional questions.
Thanks,