I don't see that as a theoritecal problem against a plausible universe having such a mechanism. We could very well create a simulation in which when you timetravel, the total energy (internal from mass and chemical bounds, external from gravity and chemical interaction with the exterior) is measured, and exchanged for exactly that amount from the source universe. If we can implement it on a computer, it's possible to imagine a universe that would have those laws.
The hard part in time-turner physics (because it's not computable) is the "stable time loop", not the "energy conservation" part (which is computable).
This is a thread where people can ask questions that they would ordinarily feel embarrassed for not knowing the answer to. The previous thread is at close to 500 comments.