Yeh, Three such circuits would do your job.
However they would each need isolation diodes in series with the circuit outputs, again to effect isolation between circuits.
Negative of PSU goes to the common ground point.
Each CC regulator circuit positive output is connected via an isolator diode (cathode terminal) to the junction of the battery and its discharge isolator diode (anode terminal).
For the purpose of Rc calculations you can ignore the effect of the diodes since they are merely a virtual resistance in the load circuit so do not affect the constant current feature.
I'd suggest limiting charge current to C/10 (300ma) in each stack, therefore your PSU must be capable of delivering at least 900ma
If you go for must higher currents then you really should have temperature monitoring on each battery stack since NiMh are somewhat prone to getting rather hot at high charge rates.