Try and get a build station mission in a nearby sector which asks you to build in the yaki sector. Or hire a transporter captain and tell him to head to yaki space and then blow him up when he arrives.
In the first instance they will destroy the station but several race cargo haulers will try to dock first and drop off there stuff. Simply blow these up and your rep will start too increase.
In the vanilla game, many, many years ago, I used to put an SPP in one of their sectors and set the price for energy to 12.
The yaki would blow up everything that entered leaving me to collect the drops. It can still be done in LU but no way near as effectively as the drop rates seem to be a lot lower. However on the upside the number of ship to ship bails is higher
