I agree with most of the comments. The BMS is not an issue. It only comes into play when necessary to prevent damage (charging below 32F, excessive charge or discharge, etc.).
I also think charging will not be a problem. Your charger will not hit 14.4V until all batteries have been fully charged. The smaller ones will charge more slowly as the larger one controls the bulk stage voltage, being the last one to let voltage rise to 14.4V. When voltage hits 14.4V, all will be fully charged.
All will likely have completed cell balancing by the time you hit 14.4V. However, some LFP batteries use a short absorption stage for the balancing. So, if any one of the batteries calls for 15 or 20 minutes of absorption, you should program that into your solar controller or lithium converter. Dragging an LFP that does not need or require absorption though a short absorption stage will not materially affect life.
What I would be hesitant about is discharging. While the differences between 12V LFP batteries (even comparing small cylindrical cells to larger trapezoidal ones) are small, they might not all approach 0% or 20% SOC at the same terminal voltage (being in parallel, they will be forced to the same terminal voltage). While the BMS is not doing anything during normal operation, it does introduce a bit of voltage drop and all BMS might not introduce the same voltage drop. Additionally there are likely some small differences in cell chemistry that affect voltage (verses SOC). I.e., since LFP batteries operate over a narrow voltage range, 13.0 to 13.3V, and have exceedingly low internal impedances, even a 0.05V difference in voltage drop among BMS would loom large. I.e., one LFP might be 60% SOC at 13.15V while another is 40%. And the battery that wants a higher terminal voltage will tend to bleed charge into the others (and thus discharge more quickly).
I'm thinking that if you don't get the bank below 20% SOC very often, you will be good enough. If you get down below 20%, one battery might deplete before the others, or at least get closer to 0% than the others. The BMS isn't going to help with this. The BMS is there for catestrophic protection and not there to avoid mild mistreatment. Some batteries like Battleborn 100AH aren't depleted until voltage hits 8.8V (2.2V per bank of cells) and surely you won't be going there!!
My long way of saying what others have. You are okay. Not ideal by any means, but okay. Still I'd avoid deep bank discharges to the extent possible.
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