I would use two-part epoxy, as it gives you working time, and it cleans up better than, and is more durable/less brittle than, super glue over time. Aliphatic resin glue, A.K.A. white/wood glue, is not a good choice. It just won't work. It's not meant to hold plastic to wood.
To clamp a finished object properly, you need padded clamps, or cauls – things that go in between the clamp and the object being clamped. Custom cut, thin-cork-lined blocks of wood are the best choice. You want a lining that is soft, yet which is not too thick, and which gets hard when compressed. I always use 1/16" cork. I guess leather would work instead of cork, though I've never used it myself. On the top caul especially, due to the nature of how fretboard inlays work (inset on a curved surface), you really want the caul to match the curvature of the fretboard, in order to seat the inlay just right as the glue sets, minimizing the amount of touchup sanding you'll have to do to get it flush. You also want to use a little waxed paper in between the caul and the fretboard/inlay, so if there is any glue squeezeout, it will glue the wax paper to the fretboard instead of the cork (much easier to remove, and won't screw up your custom-made caul). You WILL need to do touchup sanding and polishing.
In short, on first glance, it sounds like a simple job that any idiot can do, but there are special tools and procedures involved to do it ideally, and there are also 10 ways you can easily screw it up if you aren't particularly mechanically skilled or experienced. It's a $2,000+ thing, you really don't know what you're doing (you had to come ask a guitar forum, and already got at least one piece of really bad advice), it's still under warranty, and you working on it will void the warranty. And, as I already went over in grisly detail in your OTHER thread about this subject (because you apparently didn't bother to read your own warranty), this repair will likely be covered under warranty, so you can get a Gibson authorized repair shop to do it [hopefully properly] for free. It'll be simple, free, done right (or at least any screw ups will be on them, not you), and it will maintain your warranty. There's really only one prudent course of action to take, and it baffles me why you seem to be fighting against taking it. It should be done already, but you keep posting about it.
