I doesn't seem like anyone has any suggestions to offer.

I highly suggest that you try using a cleaning product by Googone. They have a product that works on upholstery really well, I've used it in the past. It is environmentally friendly, and will not damage the upholstery. You can view the product here http://www.magicamerican.com/googone/products.aspx.
Hope this helps you!

Here is a link that might be useful: GooGone Cleaners

We had a bottle of the Googone, which my dh had purchased for something. I tried it on the loveseat--ugh! It says it's non-toxic and water-based, but it sure doesn't smell like it. It was intense enough that I dragged out the Bissel Heat Pro carpet/upholstery cleaner. I am not impressed with the cleaning supplies they sell for these cleaners, so I mixed up a strong Oxyclean solution with about a teaspoon of Charlie's All-purpose cleaner. It took a lot of body English to keep the upholstery from getting too soggy--had to go over and over it, pushing down, to get all possible wetness up, but it got out clay stains (I live in Georgia). I'm too worn out to go over it with a vinegar rinse right now, but I think that would be a good idea, just in case. When it's completely dry, I'm going to open the windows and give it a light coating of fabric protector.

Bottom line: It seemed to be as much the constant flow of cleaning solution going on and being sucked back up, taking the dirt with it, as anything else.

I professionally clean upholstery, most of the jobs are spot cleaning specific stains. I have about a dozen different cleaners, some of which work only on specific stains. My go-to cleaner is an enzyme + detergent. Enzymes are good for breaking up proteins in food and "body fluids" that are the most common stains I see. I also use it when I am just doing general cleaning (last year I did a high school cafeteria that had not been cleaned in 9 years, and even then, a lot of the stains were not removed 9 years ago.) On 80% of them, that's all I needed. On tough grease stains (think 20 years of hamburgers and french fries), I used a stronger emulsifier as a second treatment.

But if you're just doing ordinary cleaning, look for a carpet and upholstery cleaning solution, e.g., Hoover or Bissell. Even a little Dawn and water would work pretty well. Do not use laundry detergents as they have "optical brighteners" that are not good for upholstery fabrics.

Before you buy anything, check the cleaning code for W or WS. I can carefully water clean about 80% of S-coded fabric. But 100% cotton, rayon or silk are not good with water.

Note too, that many of the "citrus" based cleaners work chemically like the "dry cleaning" solvents and are not effective on ordinary soiling. It all has to do with chemistry and solubility.