The multiverse would still have the same problem, unless the rules somehow change when time travelling, which I suspect they don't.
The only way to resolve, from what you suggest, wouldn't be traveling through time exactly, but use a device that created a time displacement (which is the sci-fi technology used in the Terminator franchise for instance). Time travel in this sort of way, could conceivably be possible, since it's no different than displacing 4d water in a 4d container. The balance would be, in essence, "take" something from time t1 and "replace" it at t0 and at the same instant going from t0 to t1 as a result of this time displacement. This way the Law of Conservation of Energy is not, conceivably, broken because it is still a constant value. Also, this switcharoo, doesn't necessarily have to be the same thing - but you would need some form of "anchor" for this to be possible, seeing as everything the Universe moves around a lot, planets, stars, galaxies, etc.
As for time travel without consciousness, sure, why not. People think that wormholes have this property. I'm not so sure.
The only way to resolve, from what you suggest, wouldn't be traveling through time exactly, but use a device that created a time displacement (which is the sci-fi technology used in the Terminator franchise for instance). Time travel in this sort of way, could conceivably be possible, since it's no different than displacing 4d water in a 4d container. The balance would be, in essence, "take" something from time t1 and "replace" it at t0 and at the same instant going from t0 to t1 as a result of this time displacement. This way the Law of Conservation of Energy is not, conceivably, broken because it is still a constant value. Also, this switcharoo, doesn't necessarily have to be the same thing - but you would need some form of "anchor" for this to be possible, seeing as everything the Universe moves around a lot, planets, stars, galaxies, etc.
As for time travel without consciousness, sure, why not. People think that wormholes have this property. I'm not so sure.