You can to start of pre mixing your kalkwasser in a 5 gallon bucket and only use the clear clean water after a day or so in your ATO.
You can reuse the kalk what's on the bottom again for a second time.
In that case you can just leave your pump on the bottom and you have the same effect.
Note: with less evaporation in these months you will also dose less into your tank and might need to supplement hand dosing as your ATO ain't going to cut it for you.
I like your idea better, I am short a bucket at the moment. As far as evaporation I have been seeing more, I blame it on the heat running 24/7 with the cold snaps.
BRS 50ml or any peristaltic pumps . It is out side the container :); or just tighten the cord of it so that it wont be touching the bottom of the reservoir....
You can only reuse the kalk if it didn't fully saturate your water the first time. if your water was fully saturated the first time, any precipitate would not be reusable.
Air is dryer in the winter (depending on location) and indoor temps are usually lower, creating a larger temperature differential. Both of these lead to a higher evaporation rate. Of course this all depends on location and hemisphere.
I see two to three times the evaporation rate in the winter. Refill the ATO container every two and a half to three days in winter, about every week and a half in the summer.
I use a big glass that ive fastened the pump into and sink it to the bottom of the reservoir so the water the pump draws has to come over the rim of the glass, simple and effective!