as the contactors should not care about it being sine wave driven, the H bridge approach should work just fine,
have an oscillator, divide it down to close to your desired frequency, feed that into not gate to invert for the other channel, then you could then either use a npn with a pullup resistor for each side to switch on and off the respective side, or a high side buffer chip so that it can directly drive the sides at your input voltage,
the whole theory being, part 1 of the cycle, one sides input is high, turning on the npn of the h-bridge and clamping that to ground, while on the other side its pulled low turning on the pnp and clamping the other side to +24V, and for part 2 of the cycle, the process is reversed, resulting in a square wave shaped +-24V waveform which is the same in terms of wattage as a 24V RMS sine wave,