There are a fairly wide variety of halogens to choose from, and I'm pretty sure a good amount fit your voltage/current requirements. I can't think of anything off the top of my head, but I was just ordering bulbs at work the other day and happened to be perusing the halogen section for no particular reason.
If you can't find one with the appropriate base maybe, just MAYBE, you could attempt a wild modification that I'm going to extrapolate from an LED mod I did awhile ago.
The original mod involved converting an standard
incandescent flashlight bulb into an LED for one of those old 4D-cell, single lamp flashlights that everyone has. They're bright as can be for something so simple, but as the forward voltage drops, that lamp isn't worth anything. My light has a spare bulb in it, so I decided to turn that one into an LED. When the voltage dropped I could swap the LED bulb in for a brighter beam than the regular bulb.
Basically (I can try finding the link I have saved for precise directions, if you want), you break off the bulb from the base, remove all the epoxy and glass from inside it, and solder in an LED with the negative lead to the bottom, then the positive to the appropriate resistor and then that to the side of the base. At this point you have the resistor inside the base and the LED sitting on top, which, using a 10mm LED like I did, gives you a bulb that actually looks like the original.
Now, if you can't find a halogen with the right base, but can find a cheap bulb with the right base and a 2-pin halogen with the right voltage/current ratings... Maybe you could knock out the cheap bulb, gut the base, and insert the halogen? Since those types plug into ceramic bases, I'd fill the void in the new base with something to dissipate heat buildup. And I'd test it in another socket first for heat stability.