Yes, you want to limit your battery discharge current, to 2A, 4A, or 6A.....
From your top diagram, you just need a buckboost converter, with an error amplifier to regulate its input current to 2A, 4A, OR 6A.
Why not use eg a HV9901B, and put it on constant off time mode.....then add in the error amplifier, make it "look" at the output of a current monitor in the battery supply.......and move it forward like that.
If you want to charge one batt from another....then as above, i dont know why you do this...but if you do want it...then just do the same again (input current regulated buckboost) from batt to batt.
Dont forget, any converter with which you regulate its input current, will need an output overvoltage shut-off. otherwise if accidentally started on no load, then it will go badly high voltage at its output.
You may even be able to buy a finished SMPS power supply off the shelf which gives you access to its error amplifier output....and then you just have to add the current regulation opamp etc. Try recom, tdk, mornsun, murata, vicorpower etc etc