Irreversible modification = heavily damaged resale value.
Let's calculate the cost for replacing a nut, doing a floating bridge routing & buying the bridge itself.
Cutting the nut to make space for a locking one. $50 + / - ?
Routing a cavity + drilling holes for new studs. $200 + / - ?
Assuming the spacing for a Gotoh floating bridge is suitable. $200 + / - ?
This is the minimum amount that you have to spend to get it done. of course, I'm not going to touch on colour options.
You could get a sloppy job done along with a crappy no brand floating bridge that does not stay in tune for half the price. However, what is the point of saving that kind of money when anything that is going to cost you below $450 is already considered a waste of money?
In such a case, why did you buy an Epiphone Les Paul? You should have gotten an Ibanez S series if you wanted a Mahogany bodied guitar with a stable floating bridge system. Though the tone might vary slightly, it shouldn't be too significant.
End of the day, it's your choice. Think hard.