...my suspicion is I will have to be recharging more often than I have been replacing.
Perhaps not. NiMH rechargeables may start with lower rated capacity, but they have a much "flatter" discharge rate than throwaway alkalines. (Although
this chart compares batteries with the same initial capacity, it's pretty easy to see that an NiMH rechargeable of a lower capacity could still outperform the alkaline.)
And in any event, think of it as recharging rather than
discarding.