I personally haven't colour fast tested yet, but subject to that being ok, I had wondered about a soak for a few hours and then low pressure wash off to see how much of that crap will go. Then use some tanin spotter for the doggie doo staining.
I use a very soft broom for agitation/grooming on silk... is that best or another better option?
John, your procedure sounds pretty darn close to what I would do. If the texture goes or is gone already I can generally get a good improvement with the four way groom process and a carding brush.
Is that what I cleaned a few months ago. The homeowner has one just like it in a main walk way and has completely destroyed the texture of the rug. I brought it back about 60 % but she had been washing it herself for the last 10 years.
Just wash it down, should not be a big deal. Make sure the spray of the hose is with the pile and you will not have a problem with the texture. Colors should be safe, but setting them with vinegar might be a good idea (just in case).
If colour fast is test ok; babies hair brush after soak to litely agitate; extract then check for browing or spotting probs. Good Luck; My Turkish 3x5 hand made Silk rug cost 8k just to give you an idea; and I baught it during a Port call in Turkey at a Factory tour.