@glidefloss : I think your exercise sounds great. Anything that can get the knee used to more flex is helpful. Around the same time after TKR that you are in right now I also invented a wrinkle on the standard heel slides that seemed to speed up flexibility: at the last heel slide of the series I would pause at the fully bent position, gently lift the TKR leg, point my toes, and put the ball of the foot where the heel was. Then very slowly lower the foot to rest flat an floor and just hold for 30 to 60 seconds. The tension or mild pain will subside, and the knee will get to know the tighter bend.
As far as child’s pose is concerned, I never got there. Almost. Official last flex measurement was 135 degrees, but perhaps my butt is too small to make that work for a full “touchdown”?