I've done much with batteries and some "playing" with 24V 40 Ah LiFePO4. (8s 40 Ah cells). I'm very experienced with electronics in general. I would not claim to offer you safe expert advice. Take this as competent comment at your risk.
You plan to connect the cells 4s10P with (it sound like) hard connection across each 10P bank. This is a common method and makes individual BMS "channels" 'unavailable'. It's liable to be 'safe enough' as no cell can be either driven too high or too low in voltage. If a cell loses capacity for some reason it will be maintained at a voltage equal to other cells and its current contribution will lag at the bottom end. You knew that.
At the top end its slightly more complex as a cell that reaches full capacity ahead of the others will perhaps be attempting to go into CC mode when the others are still in CV. The voltage is not up to normal CV level (typically around 3.65V). What this may mean is that a cell that is substantially sicker than the rest MAY be driven to its death slightly faster than if operated optimally - but I'd not see that as a major problem.
Operating cells hard clamped together means that you cannot determine the health of individual cells. This is common practice with Lithium chemistry secondary cells, so OK enough.
So while a BMS per cell is safest, and given the cost of the battery you are using possibly not too much dearer $% wise, it does seem that 4 BMs "channels will be enough.
LiFePO4 have, based on my observations, a mode which makes them somewhat more immune to series string imbalance that LiIon cells. While the LiFePO4 cell has a nominal final voltage of say 3.65V, if you keep charging at CC when this point is reached, rather than entering CV mode, they go into a fast voltage increase mode - ie they act as if they have much lower than their rated capacity. TI (and no doubt others) use this to advantage in fast charging - missing out the CV stage and allowing Vbat to rise at CC above 3.65 volts - but not much above. Without rechecking I think its only about 3.7V for charge termination. They claim this allows full capacity to be reached faster.
You'll probably (wisely) decide not to trust the following :-) - but it may give you food for thought. My observation, which I have not seen reported elsewhere (buyer beware :-) ) is that LiFePO4 can be charged up to normal LiIon terminal voltage (~~= 4.2V/cell). This state is approached very rapidly at CC once notional endpoint voltage is reached as the battery exhibits low effective capacity. My theory (wild inspired guess) is that while the large majority of the energy is stored in the olivine LiFePO4 structure you effectively have a small additional LiIon cell at the interface to the cell proper outside the olivine structure. It's this small LiIon cell that accepts the extra energy. The practical implication of this is that if you have say 4S cells with a target voltage of 3.65V / cell or 14.6V total, then by setting a Vbat abs max of say 14.8V = 3.7 V/cell then a cell which reaches full charge first will then increase it's voltage above nominal completion BUT in a non damaging way.
example only - 3 cells at 3.6V each = 10.8V. 14.8 max available.
14.8 - 10.8 = 4V on one cell. Actual values can be adjusted to where you are comfortable.