It’s great that you stretch twice a day every day! With all stretches (by any means) the initial increase in ROM is lost after a while, but the tissue contraction that had occurred during the period prior to stretching will be largely counteracted and the knee will more readily reach that better ROM again next time you stretch.
The stretches suggested by your physio sound quite good because there is minimal muscle use and the knee is taken through a range of movement. However, the table exercise would involve using your quads to lift the foot back up to table height, which could be problematic, and for some people may be too much. If your knee feels more painful afterwards this would indicate too much exercise has been done.
It may be difficult to do manual stretches gently enough so that there isn’t any tissue damage done. If you straighten (or bend) a little too much you can tear tissue, which you very much want to avoid. If you can do the stretches slowly and are very self-aware and stop each particular range of movement when you start to feel the tension then this may be safe and should help.
A computer controlled CPM is finely controlled to within 1 degree, and the ROM setting is only increased by 1 degree after a number of repeats at each setting. So long as the maximum ROM setting is not made too high initially and the person stops when their safe ROM limit is reached it’s very safe. But computer controlled CPMs (rather than manual controlled) are needed for this precision. Optiflex is a good type of CPM, but I’m sure there are others. Another advantage of CPM is you can sit back and watch TV while you do the stretching!
The knee pain may come from adhesions forming when your knee hasn’t moved for a while as you sleep. Then you move the knee, the adhesions are broken, and it hurts. Does this fit with your experience? Adhesions occur more when your knee is inflamed and the myofibroblasts are highly activated. Typically the problem is the worst after surgery, then tapers off with flare-ups after too much exercise.