If your flipping (huli) your yak when hooked up, be sure the rod is pointing down the hull to the bow (or stern). even if the line is pulled from the side the yak will spin and point to the fish. Then adjust your drag so the fish is pulling the yak versus pulling out line.
[Hi Dan, small world.] Your fishing sounds very similar to mine. I live in the Caribbean & troll the blue water for blackfin tuna, wahoo, various mackerel, etc and I used to use the mid-size spinners and wore out a couple of them. A wise man encouraged me to 'go big' on the reel. Here's the thing, 200 yards of line is plenty for almost everything I've ever run into. But there's also a chance I could tie into a 60# wahoo. How cool would it be to land a 60# wahoo on a kayak instead of having a fish story? The solution: overkill the reel capacity, but don't
overkill the drag setting. I replaced my Spheros 8000 with an 18000, I run a little heavier line/leader now (actual breaking strength ~28 pounds vs. 24 pounds), a tad higher drag (7 pounds vs 6 pounds), and a LOT more capacity (600 meters vs. 250). Here's what I learned, fishing is more enjoyable now, knowing that when I get a hookup, I don't have a weak link between the fish and me. I'm more relaxed to enjoy the moment. I think going high on the drag would be a bit dangerous w/ fish at boatside and definitely would take some fun out of the catch. And I'd have to build a heavier rod. If a fish can spool me w/ 600 meters & 7 pounds of drag from a kayak, then I say I probably don't want it near me anyway. Really, I'm using a reel that could deliver drag to beat a bluefin from a party boat, but I'm using it much differently for use on a kayak.
It sounds to me like your drag is set too high, perhaps to prevent being spooled. Heavy drag creates big problems on a kayak. Like Dan said, keep the rod pointed toward the bow and the drag moderate and you shouldn't have to worry about tipping over. Another bonus, the fish will tow you. Some times far and fast. This is crazy fun
, but if you start having 'too much fun' dig your feet in to the water to slow down. I did this on my last wahoo. Now, your boat becomes part of your drag and getting towed acts like having more reel capacity. Hell, I say let a fish tow me from here to St. Vincent. When it gets tired it comes home for supper!
Also, it's common to get a fish up to the boat, only to have it sound in a BIG hurry. My tuna almost always do this. This is probably the worst point for capsize. I always try to bring a fish to the starboard side of the boat (where I'm holding my rod w/ right hand), point the tip toward the bow, but let the tip dive well into the water, actually pointing the rod down a fair bit. That reduces the lever arm the fish has to tip you with. I'll let the tip dive 2' or more into the water on a hard run. At 7 pounds drag, it's very manageable, but if you try to emulate the guys on the powerboat forums and go w/ 15 pounds of drag I'd say you're in big trouble. I don't rely on hard drag to slow the fish down, just let it sound and when it runs out of water it'll play tug of war. I catch fish up to 20 pounds and only rarely will a fish get hung up on bottom (never a tuna/wahoo/mackerel). I get the feeling that a 10 pound tuna will sound if you're using 7 pounds of drag or 17. There's no sense in trying to keep it from sounding, it'll sound anyway. Once the game of tug-o-war starts, it's bad news for mr. fish. [I find 5 pounds is clearly not enough, 6 is acceptable and will work in most situations, 7 is ideal but starts to take the fun out of 5 pound tuna].