Trans-Lunar Jurisdiction: What if one of the 8 passengers (all artists) commits a crime during SpaceX's commercial flight around the moon?

SpaceX announced that the world’s first private passengers will fly around the moon in the largest reusable rocket ever to be built, the BFR. (Big Falcon Rocket)  For an as yet undisclosed amount, Japanese businessman Yusaku Maezawa purchased all of the seats on the rocket for the trip around the moon, and will be choosing up to eight artists to accompany him on the maiden commercial voyage.  Their goal will be to create an “awe-inspiring, global, universal art project,” across many disciplines, with a team including a film director, painter, dancer, novelist, musician, fashion designer, sculptor, photographer, and architect.  Recalling President Kennedy’s inspiring speech setting the United States on a course for the moon, Mr. Maezawa states: “I choose to go to the moon, with artists.”
Artists, like the general population, unfortunately are not immune from the draw to criminality, and some critics say the best art comes from a criminally twisted mind.  Additionally, a recent study found that eight percent of the US population has a felony conviction; which doesn’t count of course those who have committed a felony offense but weren’t been caught or charged.  There is a possibility, though a slight one given the rigor generally applied to astronaut candidate selection, that someone with criminal intent might be aboard this first civilian trip around the moon.
So, if while sailing around the moon, creating art to inspire mankind, a crime is committed- who has jurisdiction?  The Treaty on Principles Governing the Activities of States in the Exploration and Use of Outer Space, including the Moon and Other Celestial Bodies, (better known as the Outer Space Treaty), which entered into force in 1967, says that “States shall be responsible for national space activities whether carried out by governmental or non-governmental entities.”  SpaceX falls into the non-governmental entity category, but is a tourist trip involving artists from all over the world actually a “national space activity?”  The only company to actually send tourists into space up to now, Space Adventures has had a monopoly on the space tourist industry, sending seven people to visit the International Space Station riding Russian Soyuz spacecraft flown by the Russian State Space Agency Roscosmos.  These tourists paid over $20 million for a seat, and rode alongside actual Astronauts in the spacecraft. (NASA called the tourists ‘Spaceflight Participants’)  So while these were private citizens from all over the world paying a private company to fly, the launch and the rocket itself was under the control of the Russian Government.  Therefore according to the Outer Space Treaty if a crime was committed in the rocket on those flights, Russia would have had jurisdiction. 
While every tourist launch up to now has been through Roscosmos, and SpaceX does significant work for the US Government (SpaceX is planning to carry up to seven NASA Astronauts at a time to the International Space Station on the Crew-Dragon spacecraft) the planned art-focused trip around the moon would be the first time a purely commercial company from the United States launches tourists into space.  (Though there are others in the planning stages including Blue Origin and Virgin Galactic.)  So would the US Government have jurisdiction since SpaceX is an American company?

Maritime matters are perhaps the closest cousin to space exploration as described in the Constitution.

Most likely, yes.  While a commercial launch by SpaceX carrying paying customers might not initially seem to be a “national space activity,” there is an argument that it is.  First, this flight is paying a significant amount of the development costs of the rocket, which is estimated to be $5 billion.  Second, since the retirement of the Shuttle, American astronauts fly to the International Space Station aboard Russian rockets, (paying more than double what ‘Spaceflight Participants’ were charged) costing a total of over $3.3 billion, and launching Americans from American soil in American-made rockets is high on the priority list of President Trump’s National Space Strategy.  Third, US rockets are part of the critical components of space architecture, and therefore SpaceX conducts national space activity on behalf of the US Government when it launches rockets.
Maritime matters are perhaps the closest cousin to space exploration as described in the Constitution, and under Article III, Section 2 a crime in space could end up before a U.S. Federal Court from where the rocket was launched.  Since SpaceX is planning to launch its Big Falcon Rocket from a new launch facility it is building on the Gulf coast of Texas at Boca Chica, the Federal Court in the Southern District of Texas would likely hear any case from space on this upcoming moon mission.
So to the future spacefaring artist, remember that the law isn’t left behind when you get to leave Earth, the Southern District of Texas is watching.