Knight,
Not to be flip, Knight, but you're putting a lot on riluzole. It's not all that, alas. Diet, massage, BiPAP, kludged "comfort aids," the right bed, the right wheelchair and range of motion exercises, just to name a few, are going to have a much greater impact on your quality of life for a considerably longer period.
I agree w/ Mike that redistributing the heat/humidity isn't going to help. We lived in Houston for decades, Larry took drugs to keep his aorta from blowing out, and we didn't have central air there most of the time. Our window units were never where the drugs were. Since his pulse was kept very low by design, we would have known if the drugs were compromised. Riluzole is not inherently less stable than other orals from any research I have seen. And of course billions around the world don't have even window units.
Most often, I portioned out Larry's drugs a week or month in advance in the kind of rectangular containers that have 4 compartments per day, and rest in their own month-at-a-time stand. That way, you aren't opening and closing the bottle as often overall and you're only opening the compartment with the tablet you're about to take at the last minute.
You do want to protect the tabs from light but riluzole is otherwise labeled in the cautious UK with a 3-yr shelf life.
Humidity is more of a threat than heat for solid orals generally, which is why [deserts notwithstanding
] I wouldn't use a bathroom, but rather a cupboard on the other side of the kitchen from water (including, in our case, a 24/7 humidifier that points the other way).
Happy fireworks!