You're worried about exerting too much energy trolling a lure by paddling and yet think you're going to be able to bring in a tuna or marlin in a kayak? The guys that chase game fish from kayaks have been paddling for years, I wouldn't pedal a kayak any further than I could comfortably paddle it. Mirage drives can and have failed. Hooking up to a fish like that will almost certainly result in being towed kilometres away from shore.
Assuming you prove me wrong and hook and land one of these amazing animals you're still left with the problem of getting it to shore. I don't think you're going to want to have it sitting on your lap, even if your kayak could handle the load. Even a ~5 metre kayak is going to feel mighty small when you've got a thrashing marlin yakside. Some of the more serious offshore yak anglers have taken to fibreglass skis (Stealth, Eric etc) which can store sizeable fish in their hulls, and handle big seas. But of course the tradeoff is these require paddling, and I doubt even these craft could store a marlin.
Large tuna and marlin from kayaks remain the extreme end of the yak fishing scene, you're really breaking new ground when you target these beasts and few will be able to tell you first hand what exactly is required. Personally I reckon tag and release would be the only feasible option from a kayak, unless you're being followed by someone in a boat. I suppose if you're serious you could look into the Hobie Adventure Island with a tramp, not sure how much weight the tramp's can carry though.
If you head over to Akff.net or Kayak Fishing Down Under you might find guys that have done/attempted it, but they'd be few and far between.
Best of luck,
Adam.