Both flower, so non-flowering is a no-go with either :-)

The Lysimachia comes in a green leafed form so that's an option if you don't want to bring in yellow foliage.

And both plants are equally aggressive spreaders, the wirevine a bit more rampant than the moneywort - both will easily invade a lawn if nearby and given sufficient moisture. And I'd fear for the lotus vine surviving the thuggery of the wirevine......based on my experience with this plant, I might even fear for the boxwoods! And yes, M. axillaris is evergreen or very nearly so.

Personally, I think the lotus vine OR the golden leafed Lysimachia a better contrast with the boxwoods than the wirevine anyway but would probably limit my choice to just a single plant type. And going with that, I'd pick the lotus for better color AND textural contrast. And it's not invasive/aggressive!

Have you considered prostrate rosemary (Rosmarinus officinalis 'Prostratus')? A joy to view dripping over a wall. Easily groomed and controlled when necessary. Yes, it has tiny lavender blossoms which most gardeners find appealing both visually and when used in the kitchen for seasoning.

As stated, the Muhlenbeckia are both rampant growers and will tend to overwhelm whatever is nearby and slower growing. The Lotus maculatus is not a particularly long lived plant unless it has perfect drainage and is in a coastal influenced area that stays mild rather than extremes of heat and cold, and generally tends to die after the second year, or decline and need to be replaced. Lysimmachia also tends to be winter deciduous, so is not a year round evergreen, but something that only looks its best in the warmer months, even in USDA zone 10 conditions.

For cascading plants that would like the wet feet that you imply from the lawn runoff comment, I would be looking at plants that like constant moisture. Rosemary would be a poor choice for a wet soil site. Myoporum parvifolium 'Dwarf Pink Form' would do well here, and Rubus calycinoides would also love the situation. For a flowering cascading shrub of a scale similar to the Lotus maculatus, you might consider using Russelia equisetiformus. Pelargonium peltatum would also do well here, as long as the soil was also sufficiently porous that it didn't stay constantly wet, but also allowed air to penetrate. Lotus maculatus does not like to stay too wet, and will quickly get root rots if the roots don't also have good drainage.

I grew Lotus maculatus (the dark orange one) for several years, but removed it after repeated infestations of mealybug. It was a lovely plant, but I cannot imagine it combined with a boxwood fence -- to me that seems a clash of color and form. The Lotus is very free flowing with soft grey needle thin foliage. (And I had to cut it back now and then to refresh the look -- but I kept it going for maybe five years -- I am near the coast.) May I suggest combining it with succulents? You can pick up some wonderful color combinations using blue-green rosette-form succulents that get pink or orange-tinged tips. If the area is *very* wet, they won't like it, but they won't mind some regular water. You can find a photo of this combination on a well-known garden site run by a guy named Dave.

This photo shows some succulents cascading over a completely obscured 3 ft. stone retaining wall. The narrow space between the wall and the curb in this case is filled by Agave attenuatta. If you can imagine some Lotus maculatus in place of the bougainvillea...? Maybe this is a little too out of control for your desire for a "groomed" look?
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Thanks to ALL OF YOU but mainly to bahia. It is exactly what I was looking for.