Please forgive me for chiming in during the last day, but I would like to suggest a few more things.
This should be in 0.2A steps above 1.6A and in 0.05A steps below 0.3A (more convenience).
Lithium ion HV (4.35V) is fairly uncommon - there could be also NiZn included, as it is very easy to implement (charges almost like a Li ion, just the target is different).
For better NiMH termination, sometimes -dv/dt termination is too late, and cells are getting cooked extensively (lower currents need lower temperature limits). Will you include a method for both voltage and temperature based termination?
There could be one plastic adapter accessory included with additional springs to host some of the very small oddball li ion cells like 10180, 14230 etc.
Double d=5cm fans, and very good set of heatsinks could be necessary - (for discharging at ~16W power).
I think, these rates are only meaningful for bigger cells (21700, 26650), for smaller cells, these maybe would be too harsh.
I would suggest these:
Below 3.0V, maximum charge rate of 100mA. Below 2.5V, maximum charge rate of 40mA. Below 2.0V, maximum charge rate of 20mA.
Below 1.75V, it has to be manually activated. Below 1.5V, maximum charge rate of 10mA. Below 1.0V, maximum charge rate of 5mA.
I would also add, that for each charging bay, if a battery is inserted, but no program started, the charger is required to not drain the battery (even if it is just a few hundred microamps).
I would make this chemistry dependent.
lithium-ion: 4.05V - 4.20V
lithium ion HV: 4.15V - 4.35V
LiFePO4: 3.40V - 3.65V (I saw an article somewhere, which mentions, that at 3.4V, most of LiFePo cells are ~99% charged)
There could be more than one storage targets (different requirements). I would suggest to let the user set the target voltage in a range of 3.5 to 4.0 V (by 0.1V steps).
Storage mode could also include a discharge to the above mentioned target, if current cell voltage is above target.
I think, 4 buttons for channel quick selection (and program start/stop) + 4 more buttons could be better. Only 4 button in total could result in early button fatigue if they are used extensively.
I would add 50mA for very small cells, and 700mA is also missing.