I was just thinking about this again tonight. Perhaps a reversed release would have been ideal, with the West getting the Nov. 27, 1998 release date and Japan waiting until Sept. 9, 1999 (with games with Western appeal given priority during development). Sega Lord X argued that the Dreamcast was too early in Japan, being released when the Saturn was still in its heyday there.
Meanwhile in the West consumers were rapidly forgetting about Sega. A Dreamcast released in time for Christmas 1998 with Sonic Adventure (it came out on Dec. 23, 1998 in real life so it's feasible to imagine it 26 days earlier) would have gotten the jump on Sony and given Sega an entire holiday season as the technological leader before Sony even announced the PS2. The lack of a DVD player would have been a non-issue in holiday 1998 because they weren't yet in the same demand they would be in during 2000-2002, certainly no one would have expected one in a console. Meanwhile, during that November 1998 to September 1999 period, Japan would have continued buying up Saturns and games.
Ultimately, the PS2 would have still squashed the Dreamcast, but the damage to Sega would have been far less. Maybe Sega would have let the Dreamcast live out a full life and then retired it, going third-party some time near the launch of the Xbox 360.
Real collectors drive Hondas, Toyotas, Chevys, Fords, etc... not Rolls Royces.