If I reduce the diameter of the drain tube from the machine to the stand pipe will it not overflow?

If u reduce the size of hose from washer u will cause back pressure on motor. This could shorten the life of machine and would not stop overflow problem.

Has the overflowing been going on since machine installed?

If since installed u may have to use a closed system. This will cause back pressure, but not as much as a smaller hose.

Chuck