This report on experiments into time travel and extra sensory perception during the 1960s and 70s deserves a read.
It relates to non-physical time travel which, after years of research, I’m personally leaning towards as far as feasibility.
Assuming time is a separate dimension from the 0th-3rd, we wouldn’t be able to move in it in the third dimension (the physical) any more than we can physically move with our bodies in the 1st or 2nd.
If consciousness can move in higher dimensions, though (and we know it does, because it moves in time every moment; that’s how we perceive time), it isn’t constrained to the third like our bodies are. We already move through time, so the task would be moving consciously instead of being dragged along.
This may all be pseudoscientific bullshit, but if we can find empirical ways to test these hypotheses, I believe it’s worth exploring.