actually maybe water based stain is more accurate, though believe it involves latex believe most deck stains are like that these days. putting up lattice around sub deck, sure wouldnn't consider brush! thanks for comment bb
Latex and water based are not synonymous. Latex is the polymer used as the base. Others are Acrylic, polyurethane, etc
The basic properties of water-based coatings will remain the same based on the application; ie wall paint, stain, indoor, outdoor and so on. Diluting a water-based product will affect its drying and curing properties as mentioned above regardless of its polymer base.
I'm not familiar with anything that you are wanting to do, and I'm at Sherwin Williams all the time, including today. I rarely stain any of the decks that I build because of the waiting time. With the amount of moisture that is forced into the lumber, you can't do anything with it and expect good results for at least four months. How long has your lumber had to dry out?
As for what the people at Sherwin Williams said, I would do exactly as they said just because they know more about what they sell then anybody else does.