I've never enjoyed physical chemistry, so correct me if I'm wrong, but I don't think you're right that e-liquids for e-cigarettes require two solvents with specific boiling points in relation to nicotine. To my knowledge propylene glycol and glycerin are two common solvent choices but they are not used exclusively as a mixture. The melting point of the solvent and the melting point of nicotine is not important for vaporization either IMO. An e-liquid is contained in a closed chamber from which it is fed onto a heated coil, but the point of heating is not bringing the mixture up to boiling, but simply heat it enough so that a fraction of the solvent along with nicotine and aromas vaporizes and is then released pressurized.
BTW, the name "atomizer" is misleading, an atomizer is a device in which molecules are broken down into atoms, no such thing takes place during vaporization of an e-cigarette. In this case "atomizer" is used as a synonym for "vaporizer". Why on Earth someone came up with such use?
Whether the construction of e-cigarettes used for nicotine solutions would work for benzodiazepine solutions, I don't know. If the stability at required temperature is not an issue, then why not, but some research into dosing would be required as it is not possible to directly translate the amount of nicotine in a vapour/aerosol (solution of nicotine in gaseous solvent, it's just semantics IMO) produced by heating a given nicotine solution with known concentration in a given e-cigarette into the amount of diazepam released under the same conditions.
Anyway, I've found a patent for a device for diazepam delivery via vaporization and apparently there are numerous similar patents for different drugs.
Link here