Usual rules apply. Aviate, Navigate, Communicate, and then Manage. In this instance manage requires time to have high priority.
Management can be aided by knowledge; so find out what the capabilities of the autopilot are – I doubt that a short turn in will provide the reassuring success that you need in this instance. You have one approach, no GA (self set time limit), so get it right – expedite but don’t rush.
Knowledge of certification can be reassuring; some engine fires may not be extinguished, but they should be contained for quite some time. The structural and system design provides a margin – I won’t quote a limit, but note the Nimrod (Comet) that successfully ditched with an engine fire inside the wing after quite a long flight time. Also IIRC ’hloics quote (Canadian report) was for cabin related fires, so beware any preconceptions or bias.
The probability is that a standard emergency return to the airport (as briefed) will provide a higher success rate than attempting some unpractised, non standard, poorly planned alternative.