If you have a knee problem I don’t think you should even be thinking of using weighted hill climbs to hit Z3. The highest priority for you needs to get healed up. Until then training has to come secondary. Trying to train like you are proposing when dealing with an injury will only delay the healing process. My recommendation will be to stick with the lower intensity work while healing. This will help maintain the aerobic base you have built.
Good luck in your recovery