Hi, Hammer,
The short answer that I have is to ditch both cases unless they mean enough to you sentimentally to actually CLEAN them, otherwise it will likely come back. The long answer is "if they do mean enough, here are some suggestions on how to clean them...real good":
1) Have you looking into cleaning the leather with a boric acid and sprinkling some inside the flight case? It is the main ingredient in a lot of water damage remediation solutions used against propagating black mold spores following house floods. It is know to be fungicidal, it is pretty harmeless to people and most pets (ingestion can lead to illness, but it is weight dependent toxicity), and is already used in the process of deliming animal pelts to make leather. So, I don't think the leather itself would suffer much from treating it with a concentrated solution of boric acid to wash it, although perhaps the finish might get some checkering? I dunno, but that sounds straightforward to fix: shoeshine and sharpie?
2) Otherwise, benzalkonium salts, similar to the active ingredients in Windex or most contact lens cleaner solutions, and a peroxide, might work. This is what is in the spray-able mold ablation kits tend to use, and you can use generic Oxyclean (perbicarbonate) from the store or a monopersulfate salt (magnesium or potassium, etc.) from the internet to oxidize the mold spores with less fury than bleach or peroxide formulations after the initial application of alkonium detergents clean them out. I figure you might want gloves, but the Windex or contact lens cleaner won't be too rough on the leather.
3) Barring those choices, just wipe the leather thoroughly with a Lysol wipe to degrease it and dry clean the sonuvagun. Dry cleaning uses chlorinated hydrocarbons (non-polar molecules like tetrachloroethylene, 1,1,1-trichloroethane, and petroleum ethers, for instance) to strip surfaces of water hating/insoluble schmutz, which would be more accessible after a wipe down. This will also help strip the life out of the fungus by ripping the lipophilic components out of different membranes of the presumed Ascomycota fungi. That means that the fungus in residence is making fruiting bodies that release spores, like mushrooms, but that they also make small molecules in the spores or the fruiting body, which can be toxic to people...which is your current problem as I understand it.
I have done a lot of fungal extractions in lab, and they can be a bit formulaic, so I do think dry cleaning would actually help: usually one isolates fungal spores/material and sonicates them in an organic solvent, using a selection of ether, acetone, ethyl acetate (nail polish remover, basically), methanol, or dichloromethane (like chloroform or dry cleaning fluid). The lab I was in did sequential sonications with methanol and methanol/dichloromethane, then we'd filter the solutions, dry the soluble material down to isolate what we were looking at (which is akin to the stuff that's bugging you and your wife), and re-extract the metabolites from water with ethyl acetate. The fungus is pretty much deader than disco after the first two extractions, although state law requires bleach to be used before dumping the fungal material. Since skipping 10% bleach is a good choice, dry cleaning, which uses chlorinated stuff like dichloromethane, should bring some severe pain to the mold and may fix the problem.
So that's three ways that you can invest a bit of time or money into trying to save the leather case, if you like it enough. And, if there is fungus in the leather case, I would bet dollars to donuts fungus is also somewhere in the flight case, meaning you may have to ultimately clean it. As to your immediate health, you can ask your doctor if there is something you can do to make this case or the flight case less onerous to own while you clean it or dispose of it; y' know OTC anti-oxidant supplements, limited exposure to the cases while you decide or clean it, daily nasal irrigation, ritual sacrifice, etc. Whatever an internist would prescribe.
Or, reconsider the short answer and just get a new pair of cases if there isn't enough sentiment to warrant becoming like Schwarzenegger in Commando to clean them while quipping one-liners.
Good luck with it, please limit your contact until you have made a decision (Maybe buy some disposable N100 surgical masks? Like, seriously.), and be well.
-Zut