Have worked for airlines that had two different thoughts on the matter.
1. Shut the engine down, and carry out drills at 400agl...period.
2. Finish flap retraction, then carry out drills.
Personally favor the latter.
Suspect the B707 in question would have been just fine had the
proper engine fire procedure been followed...ie: pull the fire handle.
Actually, this is rather basic.
If pilots can't do these rather simple exercises, how much easier can it be made?