Wattage 4 or 8 ohms?

There isn't a universal answer. In my case, as per the manufacturer, the power recommendations are based on the standard 8 Ohm power rating for amplifiers, but, the manufacturer assumes that one is using a high quality ss amp that "doubles down" and suggests that if one is using a tube amp they choose one(s) with increased power output to compensate for the minimal impedance load. For example if the speaker has a 4 Ohm nominal/4 Ohm minimum impedance and the suggested power requiremnets are 50-250 Watts per channel, choose an amp that can provide between 100-500 Watts per channel into 4 Ohms. In most cases that would mean a high quality ss amp that "doubles down" rated at between 50-250 Watts per channel, or a tube amp rated at between 100-500 Watts per channel. FWIW, there is an old audiophile rule of thumb that suggests that one start with doubling the manufacturers minimum power recommendation.

Tonywinsc, Jim Thiel has told me himself that (at least with his older models) that his power recommendations are based on standard 8 Ohm amp ratings, and the assumption that the customer is choosing high quality ss amps that are capable of "doubling down". With your CS6's minimum impedance of 2.4 Ohms, I suspect your Thiels could handle well over your available 700 Watts into 4 Ohms. With that said, I'm sure your system sounds fine.

Those peaks increase exponentialy, and to do it cleanly might require a significant increase in watts. The extra power might not be required that often, but, we are talking about the "high end" here, with it's implication of the pursuit the total musical experience.

I've got no argument with you'r table. One can easily see that there is quite an increase in power from 86dB to 104dB. IMHO, and this might be more so with ss than tubes, that one would probably be better off staying away from an amplifiers ceiling of power delivery to keep the sound as clean as possible. One way to accomplish that is to have extra power at hand.

I'm sorry for getting a bit off topic here, but in some instances a higher powered amp might sound better even at volumes that could be handled by a lower powered amplifier. In some class A/AB amplifiers designs the bias of class A before going into class AB increases proportionaly to the total power output..