I agree with 411A
You are obligated to follow your company's published SOPs and your jet's Airplane Operating Manual. If those are not specific for your scenario, then you have an opportunity to decide what's best for your situation.
You say the scenario is a CAT II app below 1000 AFE with an engine flameout/failure with the standard annunciations. You say you are fully configured, have all the checklists done, and are trimmed.
For the aircraft that I fly, at this point I will also have all the checklists done and be stabilized on the approach. I will choose to continue the approach and land if I am able. The following may not apply to your aircraft, but it is a line out of my Flight Crew Training Manual specifically for the aircraft I fly:
"If an engine failure should occur on final approach with the flaps in the landing position, adequate thrust is available to maintain the approach profile using landing flaps, if desired. A landing using [normal flap setting] might be preferable in some circumstances, especially if the failure occurs on short final or landing on runways where stopping distance is critical. If the approach is continued at [normal flap setting], advance the thrust to maintain the appropriate speed. If a go-around is required, follow the normal missed approach/go-around procedures, retracting the flaps to [normal go-around with all engines flap setting]. Adequate performance is available.
Having said all of that, it continues with, "It is usually preferable to continue the approach using [engine-out flap setting]. This provides a better thrust margin, less thrust assymetry and improved go-around capability."
I will not make any changes to configuration this far along on a CAT II app. I will do the same thing that 411A says. Continue and land if at all possible.
This is just my take on this discussion. I realize there will be other points of view as well.