Many of the yellow/green varieties will establish well in full sun. Most popular of these is General Padget - massive oval leaf and easy to grow from cuttings. Yellow Excurrans is another one that will take the heat and sun all day long and even withstand a cold snap with minimal leaf drop. Gold Dust can, but usually you get a lot of blanched leaves.
For color, Dreadlocks rocks in the sun and is easy to find in the big box stores. Your Mammay looks great in the full sun, but it's easy to tell it's been there a long time. Most Mammay gets fried in the sun.
You can establish many varieties in the full sun, but it's going to take years and you'll have smaller leaves and less color during that time. The rule of thumb is "shade at noon."