The decision here rests on matching the radiological grade of knee osteoarthritis to the appropriate level of intervention in an elderly, symptomatic patient.
For mild osteoarthritis the ladder begins with non-operative measures, namely weight loss, exercise, analgesia, and selective intra-articular injections, which suit grade I and II disease. As the joint surface deteriorates and pain becomes disabling, these measures lose effectiveness and surgery becomes the definitive answer.
This patient has grade III disease with a swollen painful knee at 65 years of age, indicating advanced, generalised joint damage. The operation that consistently abolishes pain and restores function in such advanced osteoarthritis is total knee replacement. A simple arthroscopic washout offers no durable benefit in established disease, and unicompartmental replacement applies only when a single compartment is involved, which is not the case in diffuse grade III change.
Therefore the most appropriate treatment is replacement of the whole knee joint.
\[\boxed{\text{Total knee replacement}}\]