tripneustes gratillis will---but can't get the roots. This urchin is available from Foster/Smith.
What finally got my grape caulerpa, after 2 years and every cure known to man including cooking the rock---a meaningful refugium. I literally watched it fade to transparency and die. I have some growing in the fuge itself [unintentionally: my algae of choice is cheato] but it does not root in the display.
Dinoman, what urchin do you have that eats glass-growing algae?