Keep in mind that what additional power will do, everything else being equal, is to raise the volume level at which clipping occurs, and perhaps raise the volume level at which distortion starts to increase as the clipping point is approached. That's all it will accomplish.
And that in turn will depend on the size of your room, your listening distance, and the kind of music you listen to. Worst would be classical symphonic music, due to its wide dynamic range, and also obviously heavy metal or comparable rock music that, while it typically has highly compressed dynamic range, is listened to at very loud levels.
That said, I would think that given the speaker's 200W rated power handling, an amp in the area of 250 to 300W would probably be a good choice. But I'd feel free to deviate from that somewhat if it meant getting better sound quality or a significantly better price.
Concerning ICE and other Class D amps, one of their key strong points (aside from providing more watts per dollar, and reduced size, weight, heat, and power consumption) is high current capability, which does not seem particularly applicable to your speakers with their fairly benign impedance curve.
Regards,
-- Al