Almost, but I'd like to suggest an amendment to your first conclusion:
Time travel may well be possible, but unbounded backwards time travel is clearly not possible.
It may be the case that a machine will be invented that allows people to travel back only as far as when the machine was first switched on.
Similarly, a technique may be invented by which you may be able to temporarily travel infinitely into the future, and be snapped back to your present.
It may be the case that backwards time travel consumes so much of some finite resource that few or no future time travellers could possibly make it into our past.
Garry Kilworth's story "On the Watchtower at Plataea" involves a group of time travelers, from the story's "present", who push back earlier and earlier into the past... until they can't go any further because another group is coming the other way, from the past (due to the technology involved, each prevents the other from going further in their desired direction).
The "present" group then end up, essentially, in a standoff, watching the other group from a vantage point near an ancient Greek battlefield, and pointing out that they must eventually "lose" because both groups are now essentially in normal time. Which is moving from the past to the "present" from which they left.
Time travel may well be possible, but unbounded backwards time travel is clearly not possible.
It may be the case that a machine will be invented that allows people to travel back only as far as when the machine was first switched on.
Similarly, a technique may be invented by which you may be able to temporarily travel infinitely into the future, and be snapped back to your present.
It may be the case that backwards time travel consumes so much of some finite resource that few or no future time travellers could possibly make it into our past.