One should use a combo of a sequential component and a random component. When you have multiple servers, make them combine a sequential component, a unique system identifier and a random number. In this case, you can now use the faster PRNGs which will also give you speed while ensuring uniqueness.
Another takeaway from this problem is that the usual method of Multiply-and-floor has a serious flaw of using only the highest bits which may not be good enough for the default fast PRNGs. A better method is to carry forward the remaining bits from the floor using a modulo function. The default fast PRNGs rely on all of their bits and simply throwing away a big chunk is not going to help. Multiply and floor might be more useful in a scenario where you are using better PRNGs. Even then, they are slower and it is not wise to simply throw the hard earned randomness.