Well, it - is - possible to get great Custom Shop guitars from a store in Europe. You will just have to wait a very, very long time. I'm currently waiting for a Gibson EDS-1275 (double neck) from the Custom Shop. My local store in the Netherlands said they could get me one, but it would mean I would need to have patience. And the other bummer - as you pointed out - is the fact that even the store is completely in the dark. Gibson needs to sort this stuff out, especially when it comes to communication.
So, Gibson Custom Shop guitars can be of your choice...but you will have to stand in line, because you're not the only one probably. And your kind of guitar will probably be on some sort of list that all the Gibson dealers have. Mine wasn't even officially on such a list, because Gibson doesn't want to be spammed with orders for double necks. At least, that's what my local dealer told me.
Personally, I would not fly to the USA. Think about the money you'll spend extra on top of what your guitar costs. If I already had a vacation planned, I would totally do what you think about doing. So, maybe try to take some time off and enjoy the USA whilst you're at it. But to each their own. If you want the largest pool of guitars to choose from, and you're willing to make the trip, then by all means. It all comes down to how fast you want your guitar to be in your hands. If you fly to the USA, you could have your dream guitar in a few days; I'm waiting for months and months, maybe even a year.
What's also a factor, is where you're employed. See, I can't take days off right now. I'm really restricted in that regard, because I work at a university. I would have to wait for the next chance I have, which is in like half a year. Lol So, again, you just have weigh your options here. The Custom Shop Gibsons are works of art, btw. I have had the honor of playing lots of them, and they're great guitars.
Anyway, I hope this post of mine helped a bit. I guess we share some of our frustrations regarding how stuff is organized for the Europe branch. However, you'll still get a great guitar should you choose to wait for it.
Good luck