How do you operate a Li Ion battery bank between 40 and 80% SOC?

Electronics are used for Soc.

Without using a closed loop as depicted in the Schneider example, one would choose the SOC by voltage per cell then multiply by the cell count to obtain the charge / discharge setpoints of the charge controller and inverter to regulate the point at which each disconnects. The settings depend on the particular chemistry used, but using LiFePo4 as an example the fully charged state would be 3.600 VPC , multiplied by the cell count,8 in the case of 24V nominal would be 28.8V. 

To limit the charging to a predetermined SOC value, the charging voltage would be limited to 3.400V for example or 27.2V, this would result in the charging being terminated somewhere in the 90% regon, similarly the inverter LBCO would be raised to cut the discharge at a higher voltage than completely discharged  3.200 VPC or 25.6 V would be somewhere in the 20%SOC regon. These values can be adjusted up/down to achieve a narrower useage band, the cell voltage in a ballanced pack remain extremely close to one another in the normal operating voltage regon, typically ~20 mA, at the extremities the drift is more significant. Having programmable equipment will greatly simplify the process as will having a sound undestanding of the charging requirements.

Some people operate without a BMS relying strictly on equipment setpoints, though it's my opinion that this is not good practice as a BMS provides significantly more safeguards than simply SOC by monitoring the pack at a cellular level. Having the settings of the controller and inverter set below/above the BMS limitations will not affect the protection provided by the BMS but would provide protection should the equipment settings fail for whatever reason.

When dealing with lithium ion  batteries it's best to forget the theroy related to other chemistries as the characteristics are significantly different, many think it complicated but in fact it's actually not, once the fundementals are understood and the battery installed the maintenance is practically non existant.

Using the integrated closed loop equipment will save you in the education or anxiety departments  but will cost significantly more to purchase, as will using pre assembled drop in type such as Battleborne, prysmatic cells,, prysmatic CALB  LiFePo4  cells can be had for close to the cost of AGM, my latest purchase which arrived 2 days ago cost $1063 for 200Ah @ 24V nominal, add $100 for a BMS.

Voltage is a poor way of determining the SOC of any battery however in order to program  setpoints for LiFePo4  one would need to establish an approximate value which would determine the individual cell voltage and theroritic SOC. Keeping the maximum voltage below 3.650V is often recommend for solar applications though this prevents the BMS from providing cell balancing if applicable, this for the most part is irrelevant in a well balanced bank, assuming of course all cells are ballanced and  healthy.

Establishing a maximum setpoint somewhere in the 90% SOC  regon along with a LBCO  in the 20% SOC  will keep the cells within the knees of the charge/discharge curve or the "safe zone" where the majority of the useful capacity is, making.the actual usable capacity 70% of nominal. Operating between  80% & 40% SOC will result in extended cycle expectancy at the cost of lower overall capacity therefore a larger bank may be required, this is what SimpliPhi has done, they revised the setpoints thus reducing the capacity from 3.5 Kwh to 3.2 Kwh of their battery.

@softdown What I purchased are 8 individual 200Ah cells each costing  $134 which will be series connected for 24V nominal, one BMS is required. When building a DIY LFP bank to increase capacity you parrallel first then series to required Ah capacity, then series the cells or cell blocks  to achieve the required voltage, the opposite of LA. The 12V nominal Battleborne batteries are are made up of hundreds of small cells in the same manner, paralleled then series each battery with its own BMS. You're paying for the convenience of having someone build the battery, personally I prefer the larger prysmatic cells for convenience, the pre assembled 12V types usually have limitations in series connection, pre manufactured batteries can be custom made to any required voltage and capacity with on board BMS   at very competitive prices if you shop around.  The previous cells I purchased, 32×100Ah  were cheaper no name but have been in service for almost 2 years without issues these new ones are top of the line CALB with testing reports and hardware.