And no I don't understand what you mean between using a electronic timer vs a counter, again the terms you're using are generic. Do you mean a counter IC chip vs a full fledged timer circuit? No they're not even comparable what you're asking is like taking the engine out of a car and expecting to be able to drive just the engine down the street, there's a lot more than the counter to deal with, namely what's clocking it and all the other components for power switching.
I'm still confused about why you're having to reset the unit(s) every week, the quartz clocks in those things should be accurate to within a few minutes per year.