(trans)finite -> transvestite?'real' men is not enough, you need other flavours e.g.
natural, integer, rational, irrational, complex, hypercomplex, irreducible, ideal, (trans)finite, transcendental, tropical (new breed)
I can imagine the qualities of most of your suggestions, but integer men?
Have to think about that one on my way to the farm stand. :)
There could be combinations too - complex ideal transcendental, all together, for example.