That works, using a wet sponge and wet sandpaper will produce less dust than dry sanding but you need to be careful around any compound on joints. Renting a pro drywall sander would also make quick work, but you need HEPA filters on your mask since the dust is not good for your lungs.

Of all the mistakes to make drywall compound has to be one of the easiest to remove!

Soak the floor with water and use a thin flexible putty knife to gently work under the first couple. After that a stiff putty knife wil pop off the rest. Water dissolves compound so any remaining compound can be removed by soaking the compound and letting it soak in. A coarse brick sponge will be helpful.

Just soak in water and clean with a sponge. All clean in no time.

If the fibers were left after an asbestos removal project, they may not be asbestos. The asbestos removal folks who worked on my house removed a bathroom floor because the tile had asbestos in it. The bathroom was not even on the list of items to check. They found the stair treads to the basement had asbestos and several other obscure tile patches under the water heater and a washer. They really tested everything!

The most impressive part of the cleanup was the clean room approach, they used zip walls to create plastic rooms around all exposure point and sealed second chambers to get in and out. All air circulation was completely filtered with special filters. The room had to be washed down and the air filtered until a air quality meter showed a safe level of particulates for an extended period of time.

Best $1500 (1993) I spent for my family and my mental health of not having to worry any more.

Is this new? When I bought my house, we had all asbestos removed because it was said a single dose once is sufficient. It was more of a risk of how much was enough so many exposure dramatically increased the odds.