Maybe beef up the tippet? I have no experience with Cuberas on reefs but have fished Amberjacks (>30#) over wrecks with 12-14wts. A couple have gotten into the wreck and frayed the leader/stripped the coating right off the flyline but the 39# floro held. Can't say if the wreck was as sharp as a coral head. Same drill you describe which is lock up the drag point the rod at the fish and hold on...

 

At least you're vertical on them, I've found hooking up while wading is a nightmare with a number of species near any coral structures when the line goes horizontal.

Also there are "lakes" where they thrive where I see most of the hero pics come from, I believe there is a section in Randall Kaufmann's Bonefish book. In the Bahamas have been shown spots by locals where big cuberas hang out - deep mangroves cuts that are shaded and never dry at low tide... but they look disastrous to try to extract a large fish from.

I haven't fished for cubera but I would imagine they are not very line-shy from looking at their mugs, how about kevlar leader?

Maybe you could find some muttons or reds