I do not understand
you say you use AA alkalines. Okay.
You say that rechargables are not viable because "the charging frequency and effort is insane". That is where you lose me.
In the following I am making the assumption that the process of replacing the alkalines in the device is the exact same as the rechargables.
Alkaline: once a pair needs replacement you need to
1) go to storage to get new pair
2) go to device to replace spent with new
3) go to storage to place spent pair
4) return to initial location
Rechargable: once a pair needs replacement you need to
1) go to storage to get charged pair from charger
2) go to device to replace discharged with charged
3) go to storage to place discharged pair in charger
4) return to initial location
NiMH have better characteristics. If the discharge rate is low, this should be a process infrequent enough to be insignificant. If the discharge rate is high, the rechargables should make this process less frequent than when using disposables. Maybe the difference is such that it won't make a difference? Say, they last 28h instead of 26h, so you need to replace them once every day anyway, since it is likely you can't go and replace them at 2am, then 4am, 6, 8, 10 etc, you will replace them all at 7pm and be done with it.
So, what exactly makes rechargables non-viable?