With the understanding that the Loroi are rather unwilling to share high level technology, perhaps humans could get some gear from the Historians or Barsam, since both seems were very interested in Alexander Jardin Were I Earth's military leadership I would be focusing on getting better sensors as engines,  / and inertial compensators/dampers to improve the ability of existing human weapons to hit in longer- and avoiding human ships to ducks.
With the understanding that the Loroi are rather unwilling to share high-level technology, perhaps the humans could get some gear from the Historians or Barsam, since both seemed very interested in Alexander Jardin. Were I Earth's military leadership, I would focus on getting better sensors, engines, and inertial compensators/dampers. Those would improve the ability of existing human weapons to hit at longer ranges and allow human ships to avoid being sitting ducks.