Looking at your most recent picture in post #22 has the fluid changed in color from when you flushed and cleaned it the first time? Could be just the picture but it looks to me as though it too has been contaminated with moisture. You mentioned having cleaned the inlet screen, is there a cylindrical filter in the system as well?
It took me a full day to clean mine out. Even with the cover removed there were cavities that I had to spray with oil, let set and wipe clean. Like yours mine had some sludge in the bottom of the case, which as I said was actually grease from the three point lift arms. It was the sludge from the grease that had made its way to my filter that had all but blocked it off, there was no cleaning it, it had to be replaced (inexpensive).
As far as the weight of the top cover, I'd estimate mine at around 75 pounds. When removing it by hand you have to stand at the side of the tractor, and are limited in your ability to manoeuver by the rear end cast and fender. Trying to remove it from the rear offers even less manoeuverability given the need to lift it straight up until linkages clear. If you have an engine stand or block and tackle I'd strongly urge you to use it to prevent injury.
To answer your question regarding whether the linkages will work, yes, if undisturbed they will function as they had prior to your removing the cover, so long as they are not damaged during removal.