A rule of thumb is that 3KVA is equal to about 75% or 2.3KW, "all things being equal". For 24VAC at 2.25KW, you will have about 93A of current, in other words an arc welder!
An industrial fan controller should be used on the primary side, but coming up with a 240/277V model may be hard and $$$ (check industrial electrical companies for prices and availability).
Best bet, if you want to continue would be to wire it to 120VAC and use an 120V industrial fan controller or heavy variac. A transformer is designed so that at full designed load it puts out the desired voltage. As load decreases, the voltage rises up eventually reaching an open circuit value, and vice versa. A well designed transformer has alot of iron to keep voltage controlled between open and full load. Thus with 120V input and controller you would still be able atain 18VAC for rails, but you best have fuses and a fast solid state circuit breaker before the track. One derailment at 93Amps would be spectacular without those safety devices!! 
