The Jabiru engine has dual ignition coils. It does not have traditional magnetos. As the magnets on the flywheel pass the coils, a spark is generated. In theory no battery power is required, however the battery is required (a flat battery is ok) to complete the circuit.
First part is correct. Second part is not unless this particular aircraft has a non Jabiru wiring arrangement. On a standard Jabiru the battery can fall out of the plane and the engine will run normally till the fuel runs out.
As this aircraft is not a Jabiru (only it's engine) a few questions come to mind:-
Why cruise at 2,600 RPM when Jabiru recommends 2,850 - 2,950 RPM ? Jabiru does not recommend cruising at 2,600 revs You can run it at higher than 2,950 revs but it will chew fuel.
Does the aircraft cruise fast enough to provide adequate cooling?
Are cooling tubes installed to direct cool air onto the ignition coils as called out in Jabiru aircraft? If you don't have them the coils can overheat and run intermittently.
When you went to 3,000 revs did you return the fuel tap to full flow? If you didn't the fuel flow wouldn't have been enough to keep the engine going.