I'm assuming then that the lights came with the proper harnesses for H1/H4 bulbs and those are what 'still have wires'?

If that is the case, on the JDM side determine which is power and ground wire. Then do the same for the USDM harness. Cut out your USDM harness, and splice in the JDM one for each of the 4 bulbs. Wrap it with electric tape to seal out water. And you should be done.