Here is a choice that encourages specialization without punishing new players: Each company gets to select empire-wide bonuses to some industries, which can stack. So a player doing only construction is more efficient than a player doing everything.
Don’t improve these boosts with HQ levels. That way, a brand new player gets the entire boost for their whole base right away (it buffs new players) and it still encourages old players to specialize. If you make these buffs scale with HQ levels, it makes it harder for new players to compete, which is why I am against it. The #1 struggle of this game is the new player experience.
To have any impact, the buff would have to be pretty strong, at least as strong as CogC or experts are. The current faction bonuses at around 10% are not convincing many players to specialize in just one industry after all, so 10% is not enough.