A White Paper and a Blue Book
You state that
Convincing the common person is relatively easy (so easy in fact, that they would most likely start a new religion).
But the scientific community is different.
I suspect you’re wrong, and that scientists will be, as a whole, much easier to convince. That’s because the scientific community (unlike the layperson community) has a set process for establishing and proving even the most extraordinary claims.
Works like Newton’s Principia Mathematica, Maxwell's "A Dynamical Theory of the Electromagnetic Field", and Einstein’s Annus mirabilis papers were field-founding, reality-altering publications. Through precise and scientific language, revolutionary ideas were laid out for inspection, and then were examined, analyzed, and, ultimately, accepted by the scientific community.
So stop trying to prove that you’re time travelers: that’s a question of history and biography, not of science. Prove the extraordinary claim that time travel is possible.
Your question includes that as an unspoken, essential aspect that is, to the best of our knowledge, untrue in our own universe. Again, time travel is possible. That means that there are fundamental, incontrovertible physical laws that define that process, that make time travel possible, and which have demonstrable effects.
Your time travelers should publish a comprehensive white paper explaining how time travel works, along with a detailed blue-book-esque compilation of technical documents that lay out how time travel fits into the theory of relativity and the Second Law of Thermodynamics.
Lay out the entire process of how time travel was invented, from the first papers that founded the field, to the building of early prototypes that tested aspects of the theory (negative mass? Negative energy?). Since science is an iterative process, the invention of time travel would have involved thousands of collaborating physicists discovering and establishing a new and revolutionary field through countless reproducible and consistent experiments. Lay out that entire process bare to the scientific community, make it possible for them to fit time travel into their own frameworks of reality and prove to themselves that time travel is possible.
Once you’ve done that, the claim that you are time travelers is trivially believable: after all, you showed up out of nowhere with an entire revolutionary field of science developed, presented, and explored to its peak, a field that makes time travel possible.
Analogy: Trying to prove to Isaac Newton that you flew across the Pacific Ocean in a heavier-than-air plane by showing him a dated newspaper from China is a waste of time. On the other hand, lay out how his laws of motion, combined with Bernoulli’s principle, make lift possible, and then demonstrate the underlying principles and functionality of the internal combustion engine that makes the plane run, and show him the plane operating, and he’ll be much too busy being giddy about the implications of it all to have any reason to doubt your claimed itinerary.