It is very possible for the cells to be imbalanced. IME, uneven cells are unbalanced. They don't become unbalanced over time. Well, what I mean is, they can potentially get worse over time, but it's not something that you re-balance once, then all is good for awhile. The imbalance on top and/or bottom will reappear after a single cycle.
This is why I don't like the shunt resistor method of balancing. It will occur on every single recharge cycle. And it probably reduces battery life by trying to force the cells to all conform when they really won't. If I individually charge the one low cell out of 3 or 4 to bring it to 4.2, it will lag behind on the very next charge cycle, despite not using up even 1/4 of the cell capacity, right back where it settled, before. It's not something that gets worse and worse on every charge cycle.
Since you're using an adjustable DC converter and removeable cells, the simplest and most effective (IMO) thing to do is just measure the voltage of your cells after a charge and see if there's any difference.
Common sense says that the cell that is lowest is the one that isn't finished charging yet, hence it is the strongest/best. But in practice, I find this is often the cell that is weakest. Dunno the mechanism of how of why it lags behind, but it doesn't seem to really get worse over time. At least not until a cell actually needs to be replaced.
Any rate, assume you started with all 3 cells fully charged. Then after a cycle or 10, let's say you measure cells as 4.3, 4.3, 4.1.* Tweak your DC converter to be 12.3-12.4V, and this effectively solves the problem. At least the one (problem) at the top end. Whatever your cutout circuitry does, you have to also leave some margin for error on that end, to account for the weakest link. As long as you are not overdrawing the battery on the bottom end, I find the result is typically very very stable. You could also pop out the cells and charge them in single cells chargers, occasionally. Theoretically, you might object this doesn't use the full capacity of the battery, because one cell is not fully charging. I dunno; you'd have to do some tests to see what the practical difference is. I have found it's easier to just use more battery with a larger safety margin than trying to maximize cells by balancing them on every charge.
If you want to mass produce this product, then this may not be a reasonable solution. So forgive the sidetrack.