Aren't the Gold Saints in ND supposed to be the former incarnations of the ones in the original?
Not really. Officially it only applies to the Saints, Specters and certain characters (aka Sui and maybe Alone and Alta) of SSTLC.
In ND, only Tenma is said to be the former incarnations of Seiya.
I remember seeing that ND and LC where supposed to be based on the same story at some point, so it would make sense that something like that would be in both.
Off my head, the only things similar about ND and SSTLC is
- Tell story of previous Holy War
- Alone is the Vessel of Hades
- Alone & Tenma are good friends, and Tenma protected Alone
- Tenma is a Japanese Orphan (tho' in SSTLC, it was revealed later that Tenma is 1/2 Japanese and 1/2 German)
- Tenma looked exactly like Seiya
Seriously between ND and SSTLC, the story differ the moment we hit the first chapter.