Do the draining several times.  There is much more fluid in there than
comes out in one draining.  Only a flushing will get it all out.

It will take several drains and refills to completely change the fluid.  I
do not recommend a power flush that is offered by some service facilities if
the fluid has not been regularly changed according to the manufacturer's
maintenance schedule.  You did not mention what kind of vehicle you have,
but if it has a transaxle, the differential may have separate drain and
refill ports.

For about $60, you can take this to the shop and get it done in about 15
minutes, and they will do it completely, unlike what you are doing.

You need to do it several times since there is a large amount of fluid
that won't come out with a regular drain and fill. No need to go from
P to L..
Just do it 3 times and you should see clean fluid.