The kind of API I was looking for but couldn’t find (in 2014) was “when I change the value of cell A1 to 17, what’s the value of cell C5?” And get the answer within a couple of seconds. There was no supported way to programmatically change the value of a cell and get the calculated result of a different cell, at least not that I could find.
https://github.com/OfficeDev/Open-Xml-Sdk
They also support being used on .NET Core.