I love all these ideas because I don't have running water in my studio. I have to hike around our house and uphill to find a garden hose.
The smartest thing I've done is save my fancy friends' dry cleaning bags and use them to line the semicircular open surface on my Lockerbee kickwheel. I don't use a lot of water throwing, but even so, there are blops and especially trimming bits when I trim. After work I can just peel up the bag and tip any mess into my reclaim barrel.
I save coffee canisters and their lids and use a different canister for each of my clay bodies' throwing water, so I never have to clean out a water bucket. Just snap on the lid.
Instead of canvas covered boards, I work on fabric topped shelf liner (a Contact product), using a different strip for each of my clay bodies. This stuff is about three feet long by 18 inches wide (I wish they made it wider but they don't) and it rinses right off under the hose and dries quickly. It's beautiful finish for handwork. Again, I can roll up any trimming bits and carry all that mess to the reclaim cans after a day's work. (I tried to find litho fabric locally but couldn't get it for free, so I quit looking.)
I wipe up dropped clay at once. Once a week I pour clean water on the floor and suck up any dirt with a shop vac.
Still, mess and dust accumulate.
I want one of those cleaning ladies!!