I have heard that POE based synthetics have extra cleaning power, but they are extremely expensive. Redline makes such an oil.
Also, since the level of detergent in oil is important for engine cleanliness, it might be wise to use an HDEO rated oil, because they need extra detergent to cope with soot loading.
If that is all true, Redline 15w40 would make an excellent oil for cleaning.
Sometimes the easiest thing to do is use "Engine flush." You put it in your old oil, idle the car for 15-30 minutes, then drain the oil. However, there is a huge disadvantage. If an engine has a very large amount of sludge, Sometimes it all breaks free at once and clogs up the oil pump pickup. That can quickly destroy the engine.