The ,24uF is for 120V rms - For track voltages something like 3.5 uF is necessary.
My back of the envelope calculation was as follows. To get the peak voltage from RMS multiply by 1.414. Subtract the voltage drop of the LEDs (about 2 volts) from this number. Assume that the desired current is no more than 15mA, Dividing these two gives the magnitude of the Capacitive reactance, Xc, in ohms. The value of the capacitor is approximately 1/(377 * Xc). The voltage rating on the capacitor should be at last the peak voltage.
A quick web search shows nonpolar 100V 4uF capacitors sell for about a quarter each, less in quantities.
I agree that a switched sine wave will act slightly differently, but I doubt if anyone's eyes could really tell the difference.
