Just put all the techs etc in Antiquity.
The hard part there is the civ specific civics trees. Although I guess given that they have the ability to add new civics trees in other manners of the game (ie. when found a religion, the religious tree is added, or when you research the ideology civic), it's probably not completely impossible to add like a "Modern Era Civ Unlock" civic to unlock the modern era civics tree if you were playing as, say, America. At least then it's not like you're unlocking your pieces too far outside of their required zone.
And then yeah, once you add that, you could essentially have the Future Tech/Future Civic become now where you unlock the next era's tree (or you chain them so basically the exploration era tech tree just all the nodes are linked from the ancient era future tech spot).
And then yeah, if you then add in a more fluid overbuilding structure, where you can overbuild stuff even from the current age, or do something like add in a tech where each building "obsoletes" and becomes overbuildable, then you could probably chain it all together.
There's still some parts of the game even on top of that that would need some extra work - how do you handle resources, "unlocking" niter and so on later in the game? You need to fix some balance issues for the bonuses that scale with era, or bonuses that are too specific to one age (Mexico being stuck in Revolucion government for the entire game? Does Buganda get production on pillaging the entire game? Can the Mayans build their UQ all game long?)
Again, the question there certainly becomes, is it worth it from the dev side to make all those changes, spend however many months working towards all of that, for a game mode to appease a portion of the potential player-base, or are they better served putting that time into continuing to improve on the current core game model they have now? Sure, a couple of those above changes could in theory be ported or used by the current game systems to augment them, so they might not be 100% wasted. But certainly a good portion of them would not be. Plus when combined with the effort to make sure that the civs work, and to make sure that every future civ works in both game modes, I definitely struggle to see the value. I'm sure not everyone is as strict as some on what they'd be happy with from a classic mode, so if the above takes 12 months of work, and instead they take 1 month and put out a mode where the game is basically like it is now, but every civ just gets a variation that works in the other eras, while disabling civ switching, that might be enough for the vast majority of "classic mode" gamers to not spend the other effort.