Andy,
I have the after-market switch panel from Catalina Direct, also. On mine there are 8 total switches. The top one is labeled 'BOW,' the next is DECK, then CABIN, ANCHOR, RUNNING, and the bottom 3 switches are each labeled ACCESSORY. Is this the same panel you have?
On mine I changed the one marked BOW to STEAMING. Then I wired the lights to the appropriate switch on the panel.
The suggestion by Sailingdog will give you more individual control of your lights, but it's not absolutely necessary. I just have the one panel and it works fine for me.
You will want to use the black wire as the ground for both lights. Then use your green and white 'hot' wires for the individual lights. I wasn't able to follow your description of the wiring inside the lights, but you should have a jumper or similar setup between the deck and the steaming light. This would be your common ground to which you would attach the black wire in the wiring harness. The two hot wires would go to each of the two lights separately, thus allowing you to operate the lights independent of each other. Does this make any sense?