If you decide not to take extraordinary measures to save this hive, then by all means go for it. Especially if whatever you have for "standard" treatments in on hand or readily and affordably available. The way I see it is that you have symptoms of a colony that is suffering badly from disease spread by mites. There's no telling from here what "large population" means compared to your already reduced population but I'd guess your brood is way down. Brood down means that you have less mites in those cells and more exposed. More exposed means easier to treat. But, you also have a population and longevity problem. Since your sick bees aren't going to start living longer, why not treat and see what happens. I've had colonies appear to be stumbling, only to come back after a re-queening / brood cycle break.
None of this means that the inherent diseases will go away by treating with mites. You need new bees to help with that process. But, taking the mites down a few notches won't hurt at all.
"My wife always wanted girls. Just not thousands and thousands of them......"