How to finish this wiring?
Yes, your black-black strategy in the old junction box sounds right to me. 

However, I am concerned about grounds. You need to find out if this junction box is grounded.  As you have established, the left cable is only a switch loop, and therefore it must be totally separate from the other switches in that box.  The other switches must be supported by other cable(s), and maybe one of these has a ground wire back to the main panel.   It is also possible the junction box is independently grounded.   If not, then either


retrofit a ground back to some grounded point of at least the same conductor diameter as these (don't extend a ground from a 15A circuit to ground a 20A circuit).  Or 
don't connect ground wires from the lamps inside the switch box. Insulate them (don't cut them off).  The problem is if a ground fault occurs up in a light, current will have nowhere to go on ground, so it will sit there energized at 120V.  We don't want to electrify the cover plate screws on the switch! 


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You  will never be able to bury the old junction box in drywall. You can finish the drywall up to the box and install a blank junction box cover plate, but that cover plate must forever be accessible without tools.  

Also do not shorten the now-supply cable any more e.g. by snipping off old wire nuts instead of un-twisting.  You don't have any length to spare.