I think the key factors on how to get a "les Paul -sound" in a non-les paul construction are:
1. Scale lenght
24.75 scale lenght sounds warmer than 25.5. the longer scale means more sustain and more trebly sound.
Solid body Les Pauls also have a good sustain, But the attack is different if you make the neck 25.5 inch.
2. Wood
Mahogany neck and body with or without maple cap.
3. Construction
There is a difference in the sound if you compare neck through to the set neck.
Set neck is the way to go. Also the neck angle might have some effect on the sound.
3. Hardware
PAF! No other options.
Look for gibson humbuckers with alnico magnets.
4. Mass
Les paul is a heavy, thick piece of wood.
An RG-body with traditional dimensions is alot smaller. Perhaps you can stick to the original shape.
Make the body thicker, and if you can add an angled neck, then you can add a thicker top or even a slightly carved one. Thus, more wood.