Thanks guys, I'll look into it all.
Simon, do you happen to have a link to a Nashville style bridge? I come from an acoustic background, so all of this is new to me!
It's a Gibson designed bridge and they swapped to using it over the older style ABR tune-o-matic bridge when they moved their factory to Nashville - hence the name. The design stops the saddles falling out with no strings on (as happened on the ABR bridge) and as mentioned before, the saddles have more adjustment (to allow for sloppier Gibson construction methods).
Note the wider, flatter top compared to the thinner ABR type you have.
Loads of companies make them; you can chose from very cheap Chinese ones from eBay up to (what I consider the best) US-supplied TonePros ones. The only thing to beware of is that some have metric sized post holes and post screw threads (typically for guitars made in Japan/China/Korea) and some use imperial (typically those made in the US). I suspect metric would match your existing posts. But even then, some have small post holes and some have bigger post holes (typically those for Epiphone guitars). But its one of those things that your local guitar store should have in stock, so you can take your existing bridge down there and they should be able to match it for you (though they may have to order it in black).