1) Your reflector needs to be close to the lamp such that if you look across the (vertical) edges of the reflector, the lamp is "hidden".
2) the curvature of your reflector cannot match the curvature of your lamp. Think of concentric circles. Look at the left side of the drawing. The reflector is shaped (in that drawing) such that it is a portion of a circle that matches the "arc" of the circle created by the lamp profile (looking down). This means that light coming from the lamp will be reflected directly back into the lamp (at least, a significant portion of it). You do not want this.
So in the second (right half) picture, the lamp is very close to the reflector such that light originating from the lamp cannot be reflected back into it due to the angle of incidence on the reflector. It is instead reflected forward to the screen. Remember you do not have to move the lamp in this situation, at all. Just move the reflector closer to the lamp and screen, that's all. You will increase light directed at the screen by I estimate 25-30%.
I am a EE working in consulting and have done a fair amount of lighting design and attended many (architectural) lighting seminars. Trust me on this. There is an entire sector of that industry devoted to maximizing output of a light source via reflector properties.
Also I would regularly wipe off the reflector, and is it actually touching the water surface? That is big bad no no if it is.
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