unless you are an experienced woodworker do not attempt to add your own locking vibrato system to a guitar, especially a carve top.... if you really want to add a Floyd to your LP take it to a pro luthier, it will cost, but it will be done right. Installing the locking nut properly is of the utmost importance, go to someone with Floyd Rose experience... ask the shred guys at the local guitar store who they trust to work on their poodle-metal guitars. Some people do a Floyd without the locking nut and just use locking tuners, but the strings still bind in the nut unless you replace it with a self-lubricating material such as graphite or tusq. Also, if you go the locking vibrato route, be prepared for the hardware to this your tone substantially and change the balance of your guitar.
If you want to go the bigsby route and want it t be reversible and require no drilling then check out a Vibramate. Its a plate that allows you to mount certain bigsbies with existing holes on your Gibson or Gibson-alike guitar. The Bigsby won't have a lot of affect on your tone, but it will play havoc with the tension, so if you really like the way your guitar plays please keep in mind that adding a bigsby tailpiece, even one with the 'keeper bar' that adds downward tension to the strings behind the bridge, will make it so that you can't set it up to feel exactly the same as it did. That said as a former gretsch duo jet owner I can say the bigsby works very well on arch topped guitar (though I used mine sparingly and never miss it
now that I am back to LPs and 335s). Also consider a roller bridge like the Wilkinson model you see on every parts website. I used that one on my duo jet and it held tune wonderfully even after prolonged bigsby abuse whereas the stock melita did not and the bigsby bar bridge was not intonatable. A stock Gibson ABR1 or Nashville bridge is not very vibrato friendly unless you are VERY tasteful with your bigsby use (which I assume you will not be since you mentioned the Floyd Rose).
Also check out the Stetsbar, its a really great vibrato alternative that works with all your existing post holes, keeps the Gibson style bridge, but allows it to pivot like the bigsby bar bridge (only it works much better than the bar bridge). It doesn't have the vintage cool factor of a bigsby, but its a better design for Gibsons in my opinion.
Your Epiphone can use any of these designs as long as you make sure to purchase a product with metric spacing instead of Gibson USA's English system spacing. Most aftermarket vibratos are available with the import metric sizing. Hope I helped you figure this all out.
All this said, you might want to just save your beans and buy a quality LP-style guitar with a stock bigsby (check out older, used Gretsch Electromatic Pro-Jets that were made in Korea, they were very good and are not worth much). The amount of money it will cost you to add a reliable vibrato to what you have is probably more than your Epi is worth.
