The problem that you are encountering is more than trying to fit a square peg into a round hole. Adapters fix the first step of moving signal from one place to the other, but in the end, you need to change your signal as well. The video processor in your projector is able to utilize many different types of video signals, but it needs to understand what it is getting. What you are calling BNC (which refers to the connector, like RCA) is actually a composite video signal. All of your chroma and luma information is being sent down a single line. With S-video, you are dividing that information. That information is further divided when you use component video. The other problem that you will run into, is how the sync is handled. Many of the video scalers that have been mentioned have a signal auto-acquire. This helps when you don't know what type of signal that you are sending it. Even with that, you need to know how to connect your equipment. For instance, many scalers only have one type of input, the D-sub 15, commonly known as a VGA connector. Obviously you would need an adapter for your composite, s-video, or component video signal. For that you would want a break-out cable like
this (note that this one has BNC ends and comes with "bullet" adapters for RCA). The composite signal would use the green (as well as your adapted s-video signal). The component would use the red, blue, and green respectively. It has five wires since you may have some equipment that will send the horizontal and vertical sync down those lines.
I agree with museav that you would do better by scaling your lower quality composite images up and sending your signal down VGA cables instead of downgrading your computer signal and sending it as composite video. If you search the forum, you will find many recomendations for scaler devices including TVOne, Barco/Folsom, Analog Way, FSR, and many others.