Strictly speaking, the Triton Method enlarges and replaces the filter sock area of a traditional Berlin sump with a refugium type of arrangement. This is also a method pushed by the Triton company. As part of this system, the company wants to sell you lab testing so you can see your water parameters and make adjustments via dosing.
Personally speaking, this method looks a bit to questionable to me, especially when they say "... no regular water changes ...". However, I have not tried their method so I can't state that it doesn't work.
To get back to your question, I think modifying an RSM 650 sump to make it a strict Triton Method sump would require just about a complete rebuild of the sump. I don't think I'd want to make that extensive a mod to the system.
If I wanted to try the Triton Method, I think I would add a large refugium to the existing system. The Triton Method seems to want a refugium size of about 10 to 20% of the tank volume. This would likely mean the refugium wouldn't fin in the existing stand. This is not necessarily bad, since the refugium can also make a very nice display area.
Before you make any changes, consider carefully what you will gain for the amount of effort and costs involved. It you don't think it's going to be a quantum improvement, often your best course of action is to leave it alone. I hate to think of the number of times I have changed my system around and spent a lot of money only to get only a slight improvement or no improvement at all.