I am trying to figure out how to (or if I can) wire a ceiling fan and light
so that the fan and light are controlled separately -- and both are
controlled from two different sets of switches at two different locations.
The room has two doorways and I would like to be able to control the ceiling
fan and light individually from a set of switches located near each of the
doorways. This would be similar to having a ceiling light controlled by
two 3-way switches, with one at each doorway, except that in this case I
would like the switch sets to be able to control the ceiling fan and ceiling
fan light separately from either doorway.

Here is the existing wiring configuration:

The power/feed goes to the first switch setup at doorway "1" with 12/2 wire;
then 12/3 wire goes from there to the switch setup at doorway "2"; then 12/3
wire goes from there up to a ceiling light. In other words, the room is
presently wired as a typical 3-way switch setup to a ceiling light, but the
wiring going up to the existing ceiling light was prewired with 12/3 wire
instead of 12/2 in case we ever wanted to replace the ceiling light with a
ceiling fan/light. The ceiling box for the existing light was already
installed using a ceiling fan box in case the light was ever changed to a
ceiling fan/light fixture.

So, what I would like to do now is change the existing ceiling light to a
ceiling fan/light, and change the switch setup at each doorway to be able to
control the ceiling fan and ceiling individually from either doorway.

Is there a way to do this using the existing wiring that is now in place
(without using any wireless/remote devices)? If so, how would I wire that?