A great find! This is an early '60s Caballero, with the wider Epi headstock shape used by Gibson on many of their Epi models. Later examples had the hourglass headstock shape. It also has a wider neck profile than most examples from '65 or later. And it is indeed equivalent to a Gibson LG-O.
I currently have a similarly shaped '66 Epi Cortez (clone to the Gibson B-25), which has a solid spruce top & X-bracing, but also has the plastic bridge. I've had three of these over the years, and I'd offer one thought before you rip the bridge off:
If the plastic bridge is structurally stable and you truly like the tone, consider leaving the bridge on. I know what every bone in your body will think, that automatically you're going to get a monumental improvement in tone if you slap on a rosewood or ebony bridge, but I'm here to tell you (based on first hand experience), that it doesn't always work out that way. You might get a change that's more satisfying, or you could possibly get a change that is less appealing to your ears than what the guitar is currently producing. All conventional wisdom will tell you otherwise, but it can truly happen.
Now again, I say to consider this only if the bridge is structurally stable, and if you seriously enjoy the current tone. Otherwise, yes, I'd change it out in a heartbeat.