If you will post those, I will use NEC4.2 to model the whole system including an estimate of the 60' paths to r-f ground (Earth potential), and post the results.

That is a fantastic offer, thank you! This data isn't going to be as clear-cut as "120 quarter wave radials spaced with 3 degree separation at right angles to and centered at the base of the vertical radiator". Until now, that's been all of my Part 73 vertical work. I was hoping to determine the capacitance of the current top hat and replicate that using three sloping elements where the counterpoise is of a fixed value.

I understand that this is a function of surface area and distance and the slope adds an additional variable, increasing the complexity.

Of the variables you mentioned:

The depression angle for those sloping top sections - I'd go with 45 degrees. A proper value would require an exact measurement of the right triangle angles.

The horizontal dimensions of the roof - The roof contains 12 horizontal runs of varying lengths of grounding cables that terminate at iron vent pipes. Their extent below the roof is unknown.

The X-Y location of the vertical on the rooftop - The roof is shaped like a [ with the antenna positioned at the center of the open side, equidistant from the inside corners.

The operating band(s) - 1800kc

My apologies for the limited usefulness of this information. I'm beginning to realize that it's simply going to take time and experimentation to determine the proper lengths of the new capacity hat. Since there are six 6' radials at a 90 degree angle, three 12' radials of a similar diameter should present the same capacitive value. However, their slope downward will simultaneously reduce their exposed area to the counterpoise while also reducing the distance.

Fascinating stuff...