Why wouldn't you say, "That project is almost done"

In that instance I would probably say "I've (or we've)almost finished the project." Most of the time the phrase is used to question "whether it will ever come to fruition." That usage seems a bit more comfortable to me, but I may be seeing a distinction where there is none.

Thank you, everyone, for your input. Considering personal sensitivities and the fact that the statements are not public, I guess I'll just pet this peeve and keep it around for awhile.