Yes, I am saying that this is a hard limit. Read the link I gave earlier. I am not aware of anything that can move the data over as you now have an invalid NTFS configuration. The only thing that *may* work (unless you want to write a program) is to programmatically try to fool the controller into presenting the array with the original size.
It is not a matter of fixing the NTFS file system or repairing it. The file system is invalid. You will have to either programmatically fix it by getting the RAID controller to effectively lie about how many blocks are in the LUN, or to do a block-level copy of the 2.7TB onto a 2.7TB LUN, and stop it at exactly the right place, or you will end up back to where you started from.
SANtools software can drill into many RAID controllers and directly reconfigure them to settings that are supported, but not visible or configurable through the manufacturers diagnostics. If it works, then your 2.7TB lun will appear as a 2.7TB LUN then you can boot to it, then run whatever backup software you want, and/or create other LUNs as necessary to meet the size constraints. If it was me, I would make c:\ much, much smaller then create GPT disks with larger allocation sizes if you were a heavy user of large block I/O. If you do not use large block I/O, then create smaller LUNs., but read the link to understand.