I see. Something else can certainly exist, the notes can never be exhaustive. But one might assume that they would contain major points and we should extrapolate from those. Tolkien not mentioning warforged doesn't mean that them existing in the Middle-Earth is a logical extrapolation; quite the opposite.
I thought a similar thing to Neonchameleon, although didn't do the Googling.If a player really wants to play a warforged and comes up with an explanation "Feanor, Morgoth, or Saruman made a handful as an experiment" to me that would not be out of line for Middle Earth at all. It's something they might have done - and the actual world being modelled is much deeper and richer than any one author or handful of authors can convey. Just because Tolkien didn't mention something doesn't mean it can't work.
And a little googling tells me that my understanding of the themes of Middle Earth is entirely correct here and Tolkien explicitly did mention Morgoth (then going by Melkor) creating something not too far from warforged.
It's also worth noting that dwarves were explicitly made by Aule and were initially soulless. Iluvitar then objected and gave them souls.
My other thought was that I don't generally accept that a hobbyist GM's campaign setting has the same sort of intellectual and aesthetic depth and integrity as JRRT's. I think a better comparison is REH's Hyborian Age - these worlds are somewhat ad hoc "containers" for fantasy adventure to take place in.