Modifying an Old Projector with LED Bulb
I suggest that you're going about it in slightly the wrong way.
The connections to the lamp itself in a projector come from the ballast, which provides a controlled current.  In a projector (and modern, but not all older discharge  lamps) it's likely to be a fairly sophisticated ballast circuit, producing a higher starting voltage until it detects the arc has been struck.  Anyway the voltage will be high enough that you really want to avoid it.
Instead, you should probably integrate a suitable LED driver for your LED, driven off the input mains voltage (though there's a chance you could find a lower-voltage line that can drive enough current, it's unlikely).  The LED lamp bought you've may need a fixed current, or the current may be regulated within the lamp.
Cooling should be OK.  You're putting ~1/3 of the power in, but the LED lamp will be more sensitive to heat than the mercury one.
Two more concerns:

Optical.  I haven't seen, or properly looked for, an LED source that provides such an intense spot as a typical projector lamp when focussed, though there are apparently some being sold.  The total emission is less important than what it can emit from a small area in a narrow range of angles.
Bulb-checking circuits.  Many of these projectors have a circuit to check the presence and function of a bulb.  This often means that it will refuse to drive even a bulb that's electrically compatible with the drive circuit if the checking circuit isn't satisfied.  There are ways round that; with a cheap direct equivalent to the original bulb, transplanting the checking circuit onto the new bulb may have been possible, but with an LED you'll need something cleverer.