We would assume that the time-space traveler would have to tell the machine both the time and space directions from their current position in time and space. Assuming the time-space traveler cannot stop to observe his or her “location” in time-space coordinate along the way in small increments, he would have to calculate the entire travel trajectory beforehand.

I am saying this trajectory calculation relative to current coordinates is impossible. Even modern satellites with super precise instruments still need regular ongoing “adjustments.” Time travel requires many order of magnitude more precision than satellite orbital maintenance.