I would suggest using rubbing alcohol for instance to clean the stick residue on the stabilisers as well as any traces of the sticky stuff on the PCB. Make sure that after cleaning any traces you need to let the whole keyboard dry completely (use rice or better yet silica gel).
It sounds like you have not done any proper cleanup when the keyboard was affected by traces of the sticky liquid and instead let the keys get sticky after time when the board is dried. Either that or you have not mentioned clearly what did you do to rectify the issue in detailed steps. I would say that over time, expect to replace the PCB as opened can of soda in general contains things better generalised as impurities which will start affecting the PCB long after the keyboard has been dried.
As for the keys, pull them off and put them through for a wash, as well as the keyboard case if you want. Do not let any of the actual electrical component touch the water. plastic components are fine but none of the PCB stuff. Make sure the keys and all after washing a dried thoroughly (at least for a day or two) before reattaching them back to the keyboard.