We run vertical on CB because we want to work other bases and mobiles which are vertically polarized as well, and we want to take advantage of ground wave propagation for local / area work.
one minor point,groundwave barely exists at 11m as pointed out in another thread by shockwave,it is line of sight that predominates at higher hf frequencies.
a better term is line of sight or surface wave which takes in both ground wave and line of sight as opposed to skywaves used for dx.
on the whole a very interesting piece of work.might see slightly different patterns if you include the transmission line,but i realise you are limited within the confines of the modelling program you used and that wouldn't have been possible,but it does give people a good general idea of whats going on.
another minor point would be the halfwave dipole is only a good dx antenna when in free space,below that height ground reflections tend to cancel out low angle radiation and leave high angle radiation which isn't as good for dx.
like shockwave i'm also curious the effect sloping radials has on the 5/8 wave swr/impedance.i remember back in the early 80's a couple of 5/8 wave antennas having sloping radials but sadly never got the chance to try one.
i'd also be curious to see what effect upward sloping radials has on a 5/8 / .64 wave as modelled in your sigma 4 model.