Why do rechargeable batteries show different voltages?
Your description is rather unclear, but what is happening is that  the two batteries are not perfectly matched. After 300 cycles, you should expect at most maybe 90% capacity, and potentially 10% or even less depending on previous abuse. Best case, you might get another few hundred cycles from them.

If you see significant differences between on and off load voltages, this is another sign that the cells are old. A good cell will have an internal resistance of maybe 100 m\$\Omega\$, this ingreases with age.

Taking the batteries down to 1.7V will reduce their lifetime (or so I understand). Anything below 3V per cell isn't really useful. If a protected cell is dropping below its cut-off voltage, this is probably self-discharge (or a chemistry effect) occuring in the hours after the cell reaches the disonnect threshold. Unless, of course you're measuring on the outside of the protection circuit (in which case you will observe that the cell is mostly isolated).

A battery protection circuit is designed to prevent you charging a cell which has been over-discharged. This is because the cell may be damaged, and charging (particularly at the normal 0.5C rate) is likely to cause a fire.


Measure the individual cell capacities. 
Discard the weak cells (maybe anything below 60% rated value, I don't know). 
Consider how your charge/discharge application will be affected by individual cells becoming short-circuit.
If you don't understand the specific protection circuit you have, you have to assume it doesn't protect anything (cirrent, over voltage, under voltage)
Remember that lithium batteries frequently catch fire, especially when they're not used in carefully controlled scenarios.
Remember lithium batteries are not designed to be float charged (and cell-level protection doesn't monitor this)