I've owned several Thunderbirds over the years including Gibsons, Epiphones and Grecos (and a Cataldo Fenderbird). In my humble opinion, the finest of them all is the current Epiphone vintage Pro. There are a couple of minor signs giving away it's relatively low cost, but in terms of playability and tone, it's marvellous. And the build quality is excellent. I don't see it as 'just a copy', but if it is, I'm happy to play the hell out of it and proudly say I play an Epiphone. Just as you are with your Mike Lull copy 😉
Putting a Gibson truss rod cover on my Epiphone would be doing it a disservice.
Bear in mind that I've never really got on with the Thunderbird Gibson put out from the 80s onward. It was always too dark and rumbly for me. And what happened to all that glorious chrome? Of course, to many people that model is the definitive Thunderbird so it's all swings and roundabouts.