You are correct you need to get the baits down deeper to where the fish are. When you chunk, you cut up butterfish and throw 3-4 pieces in the water. As soon as the chunks disappear from view in the spreader lights you throw in 3-4 more pieces. You want to make sure you disperse the chunks so that they drift down toward your lines.
We typically on the overnight fish 5-6 lines at maximum. One line we set up for swords and send down deep (like 150-200 feet). To determine how deep to send the swordfish line you need to find the thermocline on your fish finder and then send the bait a good 25-50 feet below that level.
For tuna, we will send 1 line down 50 feet, one at 60; 1 at 70 feet and one tight to the boat at perhaps 30 feet (and about 25 feet away from the boat). As you throw the chunks and they drift down towards your lines and create the slick; they intermingle with the baited hooks. The idea is to have the tuna come along and enjoy the feast eventually to find you line.
The most important thing you can do is to post a person on the fishfinder at all times to mark the depth of the fish. If you see large red and yellow marks at 85 feet and have no lines at that depth; your odds are greatly decreased. You need to adjust your lines as you mark the fish. Many times just the adjustment of the lines can be enough to draw the attention of the tuna towards the bait. When you see the marks get your baits moving, but slowly.
Tuna have incredible eyesight. If you see their presence but can't get a bite you need to make an adjustment to your leader strength. Many times you may start with 80lb test, and then find you need to drop it to 60, 50 or sometimes even 40 lb test to entice the bite and make the lines invisible. If you think the tuna may be "line shy" you can use a tuna trap and bring the leader strength down to 40 or 30 lb test. A tuna trap is a hook "hidden" inside a butterfish with the lightest of leader protruding. Normally this would snap due to the weakness of the line. However the trap releases a cable typically 110-130 lb wire strand that isn't "triggered" until the tuna swallows the butterfish. The leader pulls on the trap (basically a lightweight rubber band around the hook and cable hidden in the butterfish). These are available from fishermans supply or direct from the manufacturer on line. I don't have their web site bookmarked on this computer, and can;t remember the company name right now... once I get it I'll add it to this post).
Hope this helps
(you can read my canyon run post stickied in this forum for other tips that may help you in your quest.) Good luck and feel free to ask additional questions. I was on vacation last week and didn't have much time to read the posts or I would have answered sooner. I'll be posting my recent Toms trip that we did Saturday into Sunday tomorrow once I get access to my pics)....