I would have the MUA as soon as possible!!
I have been in your position also, following my first TKR I had limited ROM and needed a MUA. I have actually had this procedure done twice. Like you I began looking for additional information. There are several people here that have had a MUA following a TKR and found the procedure to be very helpful, Hubbmama to name one.
Your doctor is right on track. Usually a surgeon will let a patient try on their own to reach 90 degrees until the 3 month mark. If the patient hasn't reached 90 degrees by 12 weeks then a doctor begins to get concerned and will usually want to do a MUA. What your doctor will do is they place you under general anesthesia and then pick up your leg and bend your knee. This rips all of the bands of scar tissue making it possible to bend your knee. There is no way you could handle the pain if you were awake. You have already said that PT is painful. So it is not likely that you will be able to ever get that knee bending on your own. Often a doctor will keep you in the hospital for a couple of days to manage your post-op pain so that you will be able to keep that knee bending.
Has your post-op pain been kept under control? If not people tend to (understandably) shy away from doing PT aggressively. So it is very important to have the MUA now and to have you pain managed after wards so that you are able to do your PT several times a day.
I am very surprised that your physical therapist would suggest you wait, you have already spend three months trying to get to 90 degrees. There is usually only a short window of opportunity in which a OS can do a MUA. As your knee heals after a TKR, your body is producing scar tissue. After several months the scar tissue becomes stronger than the bones or the implants and the risks of doing a MUA go up so it may no longer be an option.
In order for a TKR to be considered successful you need to be able to bend the knee 90 degrees. At 85 degrees you can not use your leg to get up from a chair nor can you go up and down steps. If your knee remains like this your doctor may want to do a revision later on. You still have plenty of time to have a good outcome and to get that knee bending. But I can't stress enough how important it is to have the MUA you really need to get that knee bending. If you continue to try and do this on your own in PT it will be a very painful process.
Once you have had a TKR the risk of infections is always a concern for your doctor. The reason infections is such a major concern is because you have a substantial foreign body in your knee which obviously has no blood supply. So if you end up with an infection the bacteria can sort of "hide" out on the implant and your body immune system is unable to fight it off. This is why we have to take antibiotic just to have our teeth cleaned. So surgeon tend to be very reluctant to open up the knee unless they absolutely need to. So normally a doctor would do MUA without the scope and then if that was unsuccessful then he may consider opening up the knee.
I think you should listen to your OS and have the MUA!!!