I am fairly inexperienced as a shooter, although have built several AR's and do a lot of reloading. Anyway, I also am an orthopaedic surgeon specializing in joint replacement at a major university hospital.
In my opinion, there is no reason why you cannot do position shooting. Sure, getting up and down with the gear and coat might be a challenge, but it is for a lot of people without knee replacements.
The only potential difficulty might be if you did sitting with your operative knee very bent and underneath your weight, which might stress the lateral ligaments.
There are some knee designs that allow more than 120 degrees, but in general most people do not get beyond this. Sometimes, a very big range of motion can be associated with loose ligaments. This can be seen with aching, soreness, swelling, or a feeling of instability going up and down stairs.
If someone with a joint replacement is still experiencing pain at ten weeks, it warrants another visit, since the most concerning issue would be a low grade infection. Some blood work, imaging studies, and perhaps taking fluid out of the knee would then be in order. without this evaluation, you cannot rule out an infection.
Persistent pain after knee replacement almost always has a cause,
some of which can be serious, like infection. Do not accept any other explanation without as a minimum the blood work and a close evaluation for infection or instability.
Finally, most academic surgeons now allow patients to kneel on their knee. If you it in a chair and bend your knee to around 100 degrees, feel the area on your lower leg that would contact the ground and you will see that your patella does not actually end up under your weight. It might me ore kneeling on your incision, but there is no data showing that kneeling on your operated leg risks injuring the patella.
Just my opinions as an academic orthopaedic surgeon. I was not going to post, but in the few years of shooting, there have been many great people who have helped me long the way, and decided to share my perpectives. Good luck.