"Drying Tent". You need air flow, preferably from the prevailing winds, so if your tent isn't just a "top", you're going to have continued moisture issues with that lumber. There's a reason that lumber producers stack and sticker out in the open with only a topper of some kind to keep direct precipitation from sitting on top of the stack. Ash is pretty susceptible to mold, especially from the dead ones. My last stack of that did get some interesting fungus on the surface, but after a few months, it gave up growing.

You may need to arrange to have the lumber kiln dried, but that's typically done after it air dries down for awhile to reduce time in the kiln. Find a local kiln operator and get their advice on how soon it can go in. You can try and spray a mold killer on the lumber but it really only deals with the surface, for the most part.