How much is "relatively little"?

You need to find out what the material is to start. Perhaps there are some tags on the upholstery and that's why they asked for Solvent or Steam? Solvent cleaning doesn't do a lot and required specialized equipment. Wet cleaning means you might have more options.
Scrub and "steam" might be an option since that's what you have for equipment. Jim England had a great video using that process. Seemed relatively quick too.
I think you need to find out what THEIR time frame is. Some of these resorts want it all done in short order because they've closed for maintenance or something.
Pricing depends on many factors:
1. What type material
2. Process used. This will determine how long it will take you to clean any given piece.
3. Time frame.
4. Competitive bid process? Someone may bid cheap just to get that much work. Don't do that.
Here are some rough thoughts:
Sofa - An hour or so to clean depending on method. Pricing? $50-$65?
Love Seat - 40 minutes. Pricing $40-$55
Recliners - 30 minutes. Pricing $30-$40
I've done some resort work before. Buildings of furnished condos. They shut the place down for a week and every contractor you can think of is in there trying to get work done. Its hectic but you can usually move right along because the stuff isn't that soiled. I'm guessing you can cut your time from my guesstimates too. The more you do the faster you get.

These are some pretty rough estimates on time and pricing. Hopefully it helps?
One thing you should give a price on is Protector. There is good profit margin in that. It might be something you can negotiate if the pricing is close to a competitors?