Sorry for the triple post, but I need some other info as well.
What does it smell like?
Rot, stinky, humid?
Nothing, humid, sweet (coconut)?
And until we can clearly determine what it is, try and swop from crickets to some Dubia Cockroaches. They tend to munch away at the fungus.
Otherwise maybe create a temporary enclosure away from the original enclosure, with just substrate (new, different brand), a clay pot or something clay for the T to hide / live in for now and then a water dish. Nothing else, keep it small, not too humid and well ventilated. Also brush the T where ever you can before you put her into the new enclosure, the fungi might be colorless to start off with.
Then clean the tank again, fill it like you would want it, humid it up and see what happens. Maybe its something in the substrate that springs up during this time of the year, though i see you posted the same thing 2 months ago, which is unusual for winter / cold.
If the old enclosure stays fungi free, as well as the spider, introduce them again to each other.
If not, you will know which to have a look at... Enclosure changing brands, or the T.
Otherwise for now, try and get some Betadine antiseptic solution (water base). Apply this to the affected spots after brushing her, 3 times a day for 5 days. After which you should be able to notice something.
If not, alch will be your best choice, though i would not recommend it as I have no idea how it will affect the T.
Good luck, and let me know

I love experimenting with mold Fungi %_%