With my first knee replacement it took me 3 years, and until I could hike 10 miles with 5,000 feet elevation change up and down, until I got past the tight band. On my left knee replacement (3 months ago), I never had the tight band feeling at all. That shows it is probably between 0 weeks and 3 years.
I think that the more muscle development you can have in your legs, the better, in every way, but increase gradually: See first post by Jockette underneath your post in the Activity Progression article. My getting over the tight band feeling on the 1st was exactly on the day I hiked 10 miles, 5,000 feet up and 5,000 feet down, but the reason why it happened that day, I don't know. Maybe it was the knee bending, or increase in muscles, or ??
Before my second knee replacement I was doing a lot of hiking, so went into surgery with well-developed muscles. That may be why I did not get "the band" feeling the second time. Or maybe there was a difference in the surgery, even though I had the same surgeon. The first surgery used a replacement knee type that conserves the cruciate ligaments, so maybe there was extra support added by the surgeon for that knee. I really did not like the feeling of a band around my knee, but by the time it stopped, I had gotten totally used to it feeling that way.
With the first knee, my replacement knee felt alien to my body, but eventually it became part of me. The more time passes, and the closer you get to full activity level, the less you will be bothered by residual elements that do not feel quite the same as before surgery. My knees are stronger and more capable, as yours is already, just by virtue of having been replaced.