Since the original post I have reset the permissions on the Machine A drive that is having issues as lined out in the Microsoft Support page
How to use Xcacls.exe to modify NTFS permissions. This appears to have kind of fixed the issue of opening, now it is just a matter of speed. There is a latency issue of epic proportions when trying to open even the smallest file from Machine A compared to Machine A opening one on the other two machines. Machine A can instantly open a huge file and it takes up to a 3 minutes to open a small file stored on Machine A via the other two machines.
After waiting it finally appears.
We have ran a PING via CMD and the machines all have equal up/down access so it is not a network issue.
So now we can open a file on the B & C machines, but it takes forever and the A Machine opens the exact same files on B & C instantly. Where does this put me other than even more confused?