First, make sure that you find R&O oil that is compatible with existing AW oil (be aware of possible additives incompatibility). Every oil company would gladly do this (test for compatibility) for you. However, if you are concern with possible bias, send samples of in-service oil and new oil in unmarked containers (labeled XZ, AZ or so) to an independent lab for testing (Herguth Laboratories Inc. comes to mind as a lab with good track record in evaluating compatibility).
Second, I would suggest you make a cutout of several pipes where you consider the conditions are the worst regarding rust buildup and sediments accumulation. You may find that flushing with new ISO 32 turbine oil would be sufficient.
Third, physically clean your sump, if possible, or at least squeegee the bottom and sides.
Acid pickling process as Christian described is OK, but should be economically justified. I mean, find out the cost of pickling, and calculate consequent potential loses due to downtime. Compare this price tag to the cost of replacing most critical segments of pipes (primarily horizontal pipes, and dead-ends) with new pipes (calculate cost of pipes, labor, and downtime). With this info in hand, you can make more sound decision.
John