I have a transfer switch rated for use on 600 volts, want to use it on 240 volts. Language in table is "Panelboards or other equipment rated 240 V and below. When used at 240 Volts, do I treat it as 240 V and below, or do I go to equipment rated > 240 V and up to 600 V?

Keep in mind how the MAXIMUM values in each section of the table are determined among all the tasks in a section. It is determined using the opening time, the bolted fault current, and the working distance listed for each section. As you move from a table rating higher value equipment especially when going from 1 kV+ breakers to 600 V class breakers for instance, the opening times will generally improve while the working distances will generally decrease. A third factor is that the "credits" taken in the table (not that I agree with them) are generally more liberal as you go for lower rating currents and voltages. The effect of these is:

Decreased opening times -- table will produce less conservative values
Decreased working distances -- table will produce more conservative values
Increased credits -- table will produce less conservative values

Considering that you CANNOT use a table if your bolted fault current or opening times exceed the values stated in the table, this is a non-issue. It is only the last issue (credits) that remains as a possible surprise. Since the technical committee's logic behind credits is not published, you are left with carefully comparing the listed tasks to see if there are any surprises that don't make sense.

Now this is a very real case for me as I'm actually in the process next week of putting a 600 V transfer switch into a 240 V circuit. The process of figuring out the bolted fault current and the opening time though provides everything I need to simply use IEEE 1584 equations in the Annex. In my case due to an upstream 50 A breaker and a relatively small transformer, the incident energy is <1.2 cal/cm^2. So I can freely ignore the table and just wear non-flammable clothing. Obviously in your case, you may get a different result but in general with one glaring exception (>15 kV), I've ignored the tables since they produce higher ratings.