Status update.
The crawl space is drying out and the mold smell is almost gone now. Which is helpful. Also getting the asthma under control. Given it's a dirt crawl and has the dead grass in it, I'm willing to bet that there's inactive mold in the soil and when you add water it comes back to life.
I strongly suspect the water came from the front corner of the house where I do have a drainage problem. The best solution (french drain) is not one I'm able to implement right now, but I have a 2nd best solution (working gutters with extension piece) in place which works great, until the bottom section of the gutter falls off and the water just dumps there. Which is what happened in the big storm. At least some of the water drained into the crawl.
At this point, since it seems to be self correcting and the electricians are due to come back in a couple weeks and make more of a mess down there, I'm just going to leave it for now. This summer I will figure out what makes sense to do - I needed to do something anyway because the floor was so cold this winter. I can't actually seal the crawl space entirely, there's no way to ensure proper airflow, so I've gotta figure out the next best option.
Re using a mask - I'm guessing you don't have asthma? Mask or no mask, my physical activities are severely limited right now. Assuming you don't have asthma, a way to get a sense of what it's like is to breathe through a drinking straw for a few minutes. I do use a mask when I've gone in the crawl in the past, and will continue to do so.