Kudos for your ambitious/expensive project, but I think youre probably going to find it very difficult to focus the beam. Especially if you would like to have a variable/adjustable beam width (which makes these light far more useful). Also, the depth of your reflector in comparison to its diameter is far deeper than what I have ever seen in any proper HID/short arc searchlight, so I wonder if it would be capable of focusing such a light source.
If this doesnt work out, maybe you could sell your project for an astonishing profit at CPF and reinvest in a 1kW AN/VSS-3A searchlight. If you are diligent in your search, you can still find them with 0-3 hours run time on the envelope (they have an hour meter that records run time). Many come with the proprietary cables, control head and remote controller. Ive paid from $350-1000 for the several I have owned. Due to their superior optical systems and design, these completely trounce a 1.6kW Nightsun Ive compared mine to. They are also extremely rugged becasue they were designed to survive at the base of a tank barrel in battle.