There are good reasons to go to numerous dealers and try to piece together your system.
The tough thing about starting from scratch is it's so hard to try out components at dealers because there are fewer than 10, 20, 30 years ago. It could be really hard to go hear the Luxman with Cornwalls together. But, the good news is you can audition them in your own space, which is ideal as you can hear them together where they will sit.
You could, for example, buy the Luxman (say L550 @ $5500) (they are superb amps) and get a new Technics 1200, and the Cornwalls. (~$4k) and jump right in. Many Luxman's have very decent (if not really, really good) phono preamps so you'd be good to go out of the gate. You could certainly buy the Luxman at a vendor like Musicdirect.com that offers no questions asked returns. Crutchfield may sell the Cornwalls with a fantastic return policy too.
Full disclosure: I have the Technics 1200 GAE and it's superb--but most owners of their own gear say that. It's built like a tank, is not prone to footfall noise, and is a dream to set up and operate.