If you arent too fussy about the enclosure, this is what I would do:
Build 2 pcb's as the design, but make one with the 712 and one with the 713.
Connect the supply to both boards, no need for a switch........ensure the charger supply can supply sufficient power for your requirements, i.e
you need 10v minimum at the minimum charge rate you have selected as determined by the resistors you calculated in the design.......
You could put the pcb's on top of one another.....stacked to minimise case size...heatsink the power transistors too!!
Tell us how you get on 8)