Nothing seems to fit

I think the Morlock theme would be edgier and more dynamic. For example, you could integrate the Time Traveler into the latter part of the game as an interference, diverting your Morlock resources to "defending against the interloper." It wouldn't be just about resource collection, but protection of your engine and production cycle.

Players build up their empire, and then once it's up and running here comes this stranger, throwing a monkeywrench in the works... That sound much more interesting to me as a player. You end up testing everyone's engines against one another in terms of resilience, perhaps even forging temporary alliances to quell eloi rebellions or other disturbances to the status quo.

Personally I'm not a fan of time travel mechanics (and especially how I've seen them implemented in board games up until now) so I'd recommend you'd stay away from that as a hook. That's just personal preference, though.

The Eloi are docile and, unbeknownst to them, raised as food. Just how docile depends on which version of the story you watch.

Assuming this is a multiplayer game, each Morlok chief is building an engine, but the pool of Eloi in the middle could be building their own based on a script/program. Without the time traveler, they only have access to stuff that helps them heal or multiply. The time traveler unlocks moves that can lead to Eloi rebelling (unlocks tied to the time traveler accomplishing goals inside Morlok territories?)

So Morloks need to leave enough Eloi to keep up their numbers, and early Eloi achievements allow for harvesting even more... but in the late game they become a potential threat so the Morloks can’t focus entirely on the time traveler.

This would be complicated to set up, but the players may be able to manipulate the time traveler somewhat (e.g., will stop current task to rescue the Romantic Interest Eloi).

Bonus points for several distinct time travelers with differing abilities (pick one from a deck) so the Morloks don’t know exactly what to prepare for.

IN the 80's there was a Role Playing game about This book. Did not last long. IN 2005 , remake of it was released by deep7 Games.

HG Wells was a wargamer and wrote two books about it. "Little Wars" and Floor Games".

There is also miniatures game for War of the Worlds in the UK. This was a custom design using old Toy Soldiers and 3D Printed Alien walkers from the Story.