I don't know of a way to clean them out of the engine.
The system used in most shops is still done with the injectors installed and with the engine running. Most systems today use a pressurized can of cleaner hooked up to the fuel line with the fuel pump disabled.
A very old system that you will probably not find in use today was the Miller system. Instead of a pressurized can, it was a cart with a small fuel bottle that you added cleaner into and it's own fuel pump. They cleaned very well, but the machines were always failing. It seems that the cleaner was so strong that it damaged the fuel pump and lines. You would be hard pressed to find one still in use today.
The correct fuel tank additive works nearly as well. I like Techron and Red Line. Some others may also work well, but I have not tried many of them. I didn't care for STP. MOC makes an excellent one, but it would be hard to find retail. MOC is mostly consumed in shops that buy their product in quantity.