I agree Oxford- i can’t stand the sight of ice plant even though it is effective in runoff and erosion. My only advice is to go to a place like Anderson’s Nursery in Point Loma by SPAWAR; in no way am I affiliated with the company!
They always give great advice, have been around for over 20 years and have a huge selection of grass and ground covering plants. Then once you get the advice- shop around for the best price.
Before you spend money on a landscaper, or drive yourself bonkers with aesthetic misery I would go there or a place similar.
If you really want to get it out- you probably want to do it quickly as we are about to start getting our rainy time- I know that sounds cheesy but its true. I don’t know whats at the bottom of that slope, but it won’t be pretty.
My next door neighbor also had ice plant on their slope, hated it, pulled it all out but didn’t replace it with anything and its true it just created a nasty mess even when she was just trying water her flowers. Needless to say- the ice plant is back.
Here are some of my favorite ground covering plants:
Creeping Thyme (There are many different types of thyme):