A modernised Commonwealth battlecruiser at Java Sea

How might the Battle of the Java Sea change if Australia deployed a modernised battlecruiser?

Japan would need heavier forces to counter it, raising losses or delaying operations even if the Allies still did not win outright.

The counterfactual assumes a surviving Commonwealth battlecruiser modernised with effective fire-control radar by 1941. Even 12-inch guns would badly overmatch Japanese cruisers, so Japan could not treat the Java Sea force as a routine cruiser problem. It would have to send its own capital ships, postpone the operation until they became available or accept higher losses. A local admiral, carrier support and Commonwealth escorts could also give the later Eastern Fleet a stronger starting core. Victory is not assumed; the strategic value lies in multiplying Japanese requirements and removing heavy units from other operations.