The best results are obtained from cleaning PP. The way I would have tackled this is as follows:-
Spray pre-spray, detergent, at 70 degrees using 400psi direct to carpet, brush in, leave for about 15mins, then extract, what doesn't improve in the doorways, like Tony says try spraying some solvent down & agitate that, then re extract, water must be hot then you should get a result.
Like I said the one I did was a wool/nylon 80/20 tufted twist which is alot more difficult to get a result and that came up as white as white can be (even I was shocked)!!
The key is good agitation, long dwell period followed by a hot (70 degree) extraction!!
(and all down by using less than 3 chems)