I know it's probably not practical for the original purpose of this post...
I think this is actually pretty practical, especially if the circuit is simplified a bit -- just two chips and some passives:
-- The first TL072 isn't doing much, is it? Just gain? Get rid of it, do all the gain you need at the same time as integrating.
-- [ Bonus: Make the the low-pass filter
second-order for improved non-spikiness ]
-- Now you've got a spare half-TL072, use it instead of the LM339. At ultra-low frequencies like this, it's going to work fine, and saves you one pull-up resistor too.
-- Don't re-generate 2.5V 3 different times, no need to keep them clean and isolated in this circuit. Especially since the right-hand side doesn't need 2.5V anymore.
Simplified circuit attached. One "trap for young players"; LTSpice's model for the D flip flop outputs 1V, which is different to a real flip flop which outputs supply voltage. No big deal, just different volume at the output.
[ All this aside, wouldn't it be simpler to just detect the presence of the input signal and output a tone of whatever frequency we choose? That'd be an even simpler single-chip solution with a 556 dual-timer. Or is the frequency changing so that it's important to maintain a relationship with the original frequency? ]