After 20 years of working with HOAs in the insurance business, I've never seen one that restricted you on working from home UNLESS you are allowing retail type traffic, or heavy shipping in and out. Which is understandable.
There's more here than we are seeing, or someone on that board is just freakin' nuts and it won't stand. To tick them off, I'd contact the HOA's own lawyer before paying for one myself.
ETA: And they also usually have to give you notice to cease such offense before they foreclose.