it could be possible to adjust tone or wording to make the important message appear routine.
Problem is disguise it as something else to appease some nervous passengers and it may not have the desired effect of getting
all the crew members attention and getting them all where they are needed, or might need to be.
As for the tone, well in this case it would seem the pilots thought they had a genuine and fairly urgent problem and I suspect even with all the PA training in the world their tone was going to appear less than routine.....
IMHO when the chips are down you just have to expend with the huggy fluffy stuff, get the job done, and sort the
PR/nervous passenger/litigious passenger aspect of it later. FWIW I doubt the incident has been accurately reported here or in the general press so the stories about the PA are irrelevant - most of the "guff" would have been posted anyway.