There is indeed a way to bias a relay coil to make it respond to a different frequency. Try contacting an Amateur Radio Group down under and see if one of their gurus can come up with the answer. It involves partial "shading" of the relay coil but without having 50 Hz available here in this rental and no way to access your particular relay for absolute "proofing" I hesitate to get specific.
Another potential source of information is your power company. Line transmission engineers have an enormous amount of experience at their disposal and they are forced to deal with the two frequency issue. The performance of the Magnum is going to take a hit working at a lower frequency. Expect a 17 to 20 percent loss of ultimate potential power. Watch for thermal issues inside the inverter until you become comfortable with it.
Best of fortune to you!