I think a Rotovac 360i would help. That is what I use and it seems on carpets like yours, I only need to go over it twice slowly with hot water at 250 psi and the carpet is clean enough to satisfy the customer.
Yes!!!!! I strongly recommend Rotovac 360i or if you want to spend a little more the larger Rotovac 360 xl. I bought the smaller one as it is more handy for my house calls, but the larger one would likely do a job like yours a little faster.
Oxifresh recommendation using a Rotary is correct, IMHO. Then follow up with a rinse. Futher, with the blue colored carpeting such as that one, the "traffic pattern" may never look, Clean, because it has been discolored by oils tracked in on the bottom of their work shoes.