Mogul base lights, along with other listed electric discharge lights are permitted to exceed the 120 volt limit up to and not above 277v. This is in 210.6(c) 1-6. It does conflict with itself, but the 120v limit is usually specified for dwelling units. I would argue that it's a special purpose area separate from the dwelling unit itself. Use 5/8 fire rated Sheetrock and rated doors to prove it to them if need be.
Make sure there's no local codes against it first, I doubt there will be. Get in touch with the AHJ in your area if you can.