So the basics to start here is my process as I follow it. Keep in mind I use a HWE. So if your using a LGCM or something similar your going to have to work a bit more.
1) 1)dry vac
2) dry vac again.
90-95% of the soils in the fiber are dry particulate dirt, best removed by dry vacuuming. if you add moisture to a poorly vacuumed fiber/carpet you have to work 10 times harder than needed with 10 times the amount of chemical and water than is needed. With 3-4 times the drying time. So dry vac very thoroughly. Use multiple attachments.
3)Pre treat stains and spots.
Why do this now? Because stain removers work best when applied to virgin stains, In many cases if not all that i can think of right now detergents will inhibit the stain removers if applied before the stain remover. So spot treat trouble areas first, Buy specific products for those areas. lightly rub them in and let them sit while you prepare you chemicals for the main area.
This is where you evaluate your stains:
If it is an oily, greasy, grimy but not food based stain dab it with citra-solv and gently agitate it thoroughly through the fiber.
If it is a food, or protein based stain then add the bac out stain remover. Agitate carefully into the fiber. Let sit 5 to 10 min .
4) Pre-condition the fiber/carpet with cleaner.
use a proper cleaning product. Read the dilution ratio's More product is not better or, lower dilution. These products work in conjunction with water, improperly mixing them will provide very poor results. Normal carpet cleaning agents are 32 parts water to 1 part solution. Once applied Brush in with your brush or PC if you feel the need. Despite what you think agitation will not improve your dirt removal. In many cases you'll keep the detergent from working by agitating too much. In some cases you will distort the fiber. (velvet it) The purpose of agitation is not to break dirt free, but to get your cleaning product to as much surface of the fiber as possible. So light agitation will suffice.
This is the area where you decide which of the two pre-conditioner/traffic lane cleaners to use.
If it is a oily soil, grease, shop gunk, mud, or plain dirt use ultra pac with lvc.
If it is more of a kids dumped all their frys, shakes, soda, pizza hamburgers, fish crackers car then use bi-o-kleens traffic lane cleaner.
If it is the head liner or seats then use fine fabric shampoo. (I will type up an addendum of how to approach these properly)
5) Extraction,
You can use a bonnet method i mentioned above, think Chem-dry the nationally owned chain.
You can extract with shop vac and 1/2 gallon pump sprayer of clean water or water 1ith 1/2 oz of vinager mixed itn
You can extract with LGCM or similar tool.
You can extract by buffing with a towel.
You can use a HW extractor.
The key is to get the fiber clean, then get it dry as possible, then get it set up for the shortest drying time as possible.
In this case the is where you put in your dry slurry mixed rinse agent and extract. This will remove any final pre-conditioners, spotters and any remaining soils leaving the fiber prepped for protectant.
6) Applying the protectant. Here is where you apply the protectant to seats, headliner, and carpets. I was unable to give you a huge amount but it should be sufficient to do one sedan. Mist it on the carpet, seats, and headliner. Then with a clean white terry, dry stroke it to work it into the fibers. 1 16oz bottle should do a sedan so try and space it out accordingly.
7) Drying.
There is little air movement in a car, So turn the fans on crack the windows, set up small portable blowers. The faster you get this dry the less soil wicking you will have. Adding significant air movement and ventalation will cut drying time in half if not by 3/4. Adding the bonnet buffing i mentioned befor can make even a HW extracted carpet dry with in 45-1 hour of finishing.
Using the fine fabric shampoo.
This is actually a shampoo. It is designed to make vast amounts of suds. It is made for fine fabrics. IE silk, hatian cotton, ect ect. You can spray it through a spritzer and brush it in with a horse hair brush on the seats with out worry. Then simply extract them like you would the carpet.
However it is different for the headliner. Here I recommend using a super dense grout sponge. Dip it in your mixed solution. Wring it 80% of the way dry. Then massage it back and for the like an accordion. This will generate a dense lather. Gently brush the lather onto the headliner with the sponge. Then wipe dry with a clean MF or Terry towel. Repeat this through the whole headliner. It may look blotch but will dry with out water marking. That is to say. If you only clean with foam resist the temptation to clean with the wetness of the sponge. If that happens dampen a terry wring it out and wipe the whole headliner down then gently vacuum and set up air movers to dry.
This is really frustrating, I bet the area in question isn't more than 3" x 10" or so, you'd think that a few hours of work would've done it, but no dice.
) but I doubt if its getting the water that warm. Would you change your product suggestions based on the fact that many of us don't have access to a good extractor. Thanks for the information, I always enjoy reading your posts.
It just grosses me out..the areas where the dogs ride always clean up like new; it's pretty bad that *I* am responsible for the worst problem with the dog car 
) and see what I go with.