Hang in there and please do continue to ice and elevate a lot!!!!
My late January TKA had exactly what you describe: within ten minutes of being in any position, it was uncomfortably stiff. Until after week 12, getting out bed in the morning required support from both hands and the other leg; it was excruciating for about ten minutes.
Two things I found really helpful: before changing position, place one hand on each side of the knee and slowly, gently move it through its current range of motion, without any stretching, for a couple of minutes, then slowly walk in the house for 5 minutes.
I will note that at over 6 months out, while it's quite a functional leg, there is still minor stiffness after being in one position for a while (definitely tolerates more than 10 minutes!).