Oil on brakes

The first thing I'd do would be to remove the drain plugs at the bottom of the steering clutch/brake compartments and see what comes out. Let 'em drain, replace the plugs and fill the compartments to the a little above the bottom of the brake bands with diesel or kerosene. Run it back and forth a bit w/o using the steering clutches to wash the bands and drums, tap the brakes a few times and drain again. Then run it back and forth some more while riding the brake gently to dry 'em out. Run the critter some more after replacing the drain plugs and see if you can find where the oil is coming from. A good place to see is after you remove the two inspection plates at the back of the tranny behind the steering clutch/brake compartments.

thats definately a good start.
might be worth checking your transmission oil to see if its dropped at all as well.
you say you were clearing in steep country so theres a chance oil was weeping through the diff axle seals.
the other spoit the oil can come through is from the final drives, so it might be worth popping off the hex bungs on either side at the rear
of the dozer. they are the oil fill points for the final drives.

The oil seem to be only on the linings themselves the backing plates are dry and there doesn't seem to be oil anywhere else in there when it's cold or you stop for five the brakes work well but when you work it for a while they get worse