I use Audio Intelligent three step cleaning system, the second step being Archivist fluid, with Okki Nokki vacuum cleaning machine. The results are excellent, though I never tried extremely dirty records. Nor did I try any other fluid. When I bought the AI from Needle Doctor, the man I talked to said that he slightly preferred it to Mo-Fi.
Sometimes I use step 1 or even step1+step 2 twice if I feel the record is quite dirty, and I always use step 3 - pure water- twice. Disc Doctor brushes, three of them of course. Also, sometimes I let the solution 1 and 2 to stay on the record for a few minutes after spreading it before vacuuming it off. I get very clean records. You can probably do better than that, but the records are clean enough for me.