I would stick to the 998 timeline, but I'd go whole-hogged and make Eberron a massive module for pulp-adventure games. So, not only would Eberron be a new setting, but an entire module dedicated to playing D&D in Eberron.
You can reprint and hammer home the basic themes and a lot of the location material, but then also include tons of alternate rules, character options, etc. that take someone's D&D game and really spin it and make it into a unique experience. As it was in 4E and 3.5, Eberron was basically something you tacked onto D&D. Sure, you had some new feats and classes and the "Action Points".
But, Action Points? Seriously. That's what is going to give Eberron it's feel mechanically? I don't think so.
If you're going to reprint the setting, do it so that when we buy it, we have options that we can add to the core rules that change the game fundamentally, and make that change tailored to Eberron.
As it stands, it seems like D&D5e is going old school. But, Eberron campaigns transcend that style in a lot of ways. Give rules for pacing and intrigue. Factions and espionage. Hell, give the DM some rules for status and reputation tracking for patrons and players in the setting. Give us tools and advice for putting together a satisfying campaign with multiple twists and turns. How should we run a sandbox in Eberron? How do you do that? How should we?
Are there bits of the core game we can change to make an adventure or campaign feel like Eberron more?
That's what I want. I can read all day long about the next new place or NPC or whatever. But, that might not be something I can use in my game right now. There are only so many places I can highlight in my campaign and dedicate time and story to. However, I can always use more ways to make my campaign more Eberron.
With 5E's modularity, it seems like the perfect fit to really expand the game and say, "If you buy this setting, your game will ooze pulpy, train mystery, Indiana-jones style action adventure goodness because we've added rules and options to help you get that feel out of the D&D Next rules set."