Nicholas, I cannot speak to the various ICs: I don't know squat.
I'm using one of these to handle charging my batteries (2x 6v SLA in series):
https://www.batterytender.com/products/battery-tender%C2%AE-5-45w-automatic-solar-controller
In Los Estados Unidos, hunting is quite the thing and in my area, deer hunting in particular. It's common to use dispensers to throw corn for the deer and those dispensers commonly run on 6 volts (and some on 12v). Small, 6V, 5Ah (or similar) SLA (sealed lead acid) batteries are easy to get from many stores, not to mention online. I have two of these in series from a southern-engineered (bricoler) project last year. These batteries cost me about $10 each as I recall. You mention 18650 batteries: a lot of this is subjective, there aren't "right" or "wrong" answers but my take on that is this: solar panels charging 12v SLA (and similar) batteries is a totally common thing (also think: car battery tenders with solar panels). I would stick with that solution if for no other reason that there are tons of materials and users so it should be easy to source well-tested solutions.
--HC