Finished a full discharge and charge test of the Leaf module (in 7.4V configuration) in parallel with 2s2p Boston Power Swing 5300 cells. The discharge test was done at the max power of my tester, 60W, which means current did vary as the battery voltage dropped. The charge was done at 5A, which is a bit lower than an L2 charge (~8.8A). I performed the charge termination at roughly the same level I've seen my car stop charging at, which is about ~1-2A in CV mode. Here's the discharge graph:
So exactly as Mux found, the extender pack (in my case using LCO chemistry) delivers most of its energy toward the end of the discharge curve, which means it is providing a majority of the power towards the end as well.
Just between turtle and dead, the extender pack took the maximum proportion, about 58.1% of the total current, meaning it would have had to provide 159A, which is way more than the 26A rating of 2 Swing 5300 cells in parallel. Basically, this limits the minimum extender size to at least 12-13p, or ~17.3 kWH usable for this model of cell! Taking the calculation for a higher drain cell, the LG HE4 (which I should be getting samples of in the next day or two), the minimum extender size drops to 8p, or ~5.4 kWH usable.
The charge curve is nearly the inverse, with some bumpier behavior at the start of the curve. In charging, the BP cells took a maximum of 52% of the charging current, which again would be an issue in DC fast charging, limiting the minimum pack size to 6p of the Boston Power cells, or 16p (~10.9 kWH usable) for the LG HE4 cells, in order to take the ~65A that would be coming from the charger.
Early conclusion from this data; it's better to go with hybrid or EV batteries that are already sized/designed to take such large charging/discharging powers, if using a cell chemistry other than LMO. Otherwise, you can use "standard" Li-Ion cells but you will be building a very large pack (at least 11 kWH sized), and we still have the SoC estimation problem to resolve.