I saw the Les Paul signature and I love that body style with the offset horns. Sort of a hotter looking Guild Starfire or Gibson EB2. I once owned a used Casady. The only complaint I had with it was the finish was cheap and tended to chip very easily. On the other hand, I played a used LP signature while I still owned the Casady. Though the signature was clearly a much better piece of workmanship, I thought the Casady electronics performed better out of the low impedance set up. The new, bigger soapbar seemed a lot hotter than the old Gibson pu.
Admittedly, I didn't A-B with the same rig. Also, I can't vouch for the condition of the LP I was playing. But when I got home and played the Casady (through my own, lesser rig), it sounded better to me. Better clarity and definitely more mid and bottom end punch. I finally let go of the Casady because I had just gotten my first Alembic and wasn't playing it a lot. But I really liked the Casady and thought it was a good deal at the used prices you can find if you're patient (I think I paid $375).
The LP on Ebay looks like it might have some historical significance if it actually is a prototype, rather than a production instrument. But for the money and the sound, the Casady is a pretty good deal and fun. I'm sure I'll buy another one eventually. The one thing I might do with it is use some sound deadening material inside to reduce the tendency to feedback (I know it's sacriledge, but forgive me).
Bill