Paul,
The label clearly indicates how helpful the manufactures wishes to be.

Of the three fibres mentioned, nylon micro-fibre (Antron) is the most likely.
Solution No. 4 would be suitable but may need a little help - a
very light misting of Eco Spotter on heavy body contact soiling immediately after the M-S can have amazing results. The agitation of heavily soiled areas is best done with an upholstery mitt or cotton towel.
These fabrics greatly benefit from a towel finish - if the towel turns grey, more rinsing is required, followed by further towelling.
Before you start you should discuss the probable removal of the fire retardant by the cleaning process.