Exactly what I was thinking. There is/was a WARL presidents meeting tonight with the main topic being whether there'll be a 3rd grade comp this season or not. With the Colts comp folding, there is an excess of players not getting a run in either First-Grade or Reserve-Grade for most teams, so there is a very strong chance there will be a 3rd-Grade comp starting within weeks. You may be in luck.
But like PerthRed said, you are most likely to get a run with Willagee than anyone else. They are struggling big time (having about 100 scored against them most weeks so far in First-Grade, and big scores against them in Ressies).
Willagee is down towards Fremantle though, so it's a fair drive from the North Beach area (about 40mins I suppose).