tech2000my, I think you may have misinterpreted the rated voltage for the solenoid - 110 to 180 volts looks like minimum and maximum voltages to operate, rather than a range over which the voltage must be varied. If that is so, any voltage in that range should work.
Correct me if I'm wrong folks, but I'm thinking, if the need to vary the voltage is actually bogus, won't a single series rectifier in the live wire do the job? Just means the waveform won't be sinusoidal, but a small snubber capacitor would take the corners off at least, and to operate a solenoid that shouldn't matter.