One thing I forgot, the stiffness and swelling is not totally unexpected at 3 plus months, even for someone like you doing everything right. Chris's advice on building up walking is excellent.

I didn't have these problems, but I bike rather than walk a lot. I did have a friend, in great pre-surgery condition, and his knee was stiff, sore, and swollen for a good 5 months before it started to get better.

So we're all different. Stick with your plan. A very good device to cool your knee is the Hurt Skurt (or Skirt) - you can get one on Amazon. Stick it in the freezer then just pull it on. It surrounds the knee and helps.