switching solenoid through transformer
There should be no problem using the transformer to adapt the 120VAC down to use by the three 24VAC valves. Just make sure that you select the transformer with adequate secondary current rating to supply the three valves. 

Do take a look at the thermostat though and make sure that its output switch or contacts are capable of handling the load of the one valve plus the transformer. All of these loads are inductive and can arc contacts if mechanical switches or contacts are in use.