Agitation is the only method that brings sand to the surface. I use my PC with the green bristle carpet attachment brush. If possible pull the carpet up from the end where it's tucked under the pedals and door thresholds and pat the carpet backing. This with the helpbof gravity will get at least half the sand/particles out if the carpet. Extraction helps lift the ultra fine particles by wicking as the carpet drys. Once dry vacuum again and go another round with the extractor if you feel it's necessary. Wiping when dry and blotting the carpet when wet helps pull away some particles close to the surface of the fibers but will do nothing for imbedded sand/particles, IME.
Like stated, it is just a time consuming process to get every bit of sand out of carpet. Your best bet is talk to the customer and advise them that it be an ongoing process with maintenance details. Otherwise you lose money on your time spent or the customer will pay a lot more initially. Of you can pull the carpet completely you flip over and knock the sand out. All depends how much time you have to spend on the vehicle and what the customer's desire is.
If you don't have a carpet attachment for a DA then using a stiff bristle brush and sweeping will help a good bit. I use a dust pan broom/sweeper that I bought from HF.
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