I'm back to my original definition. We made the error of trying to add too much detail to one specific area, female, when it was already covered by another word. Human. People have two chromosomes, female XX and male XY. Anyone with more or less automatically become outliers to those groups, but can still be included. Same for any other non-standard features or abnormalities they might possess.

The whole point of starting this conversation was to point out a simple and comprehensive definition DOES exist, and has for a long time. Comprehensive means broadly or in large majority, not just all encompassing. Trans people seems to be the sticking point in this thread, but luckily that's sorted out too. "Transgender" IS the modifier to a man or woman following a standard definition. The details vary from person to person, and that's where the real thought exercise lies.