A soldering iron will generally be way too hot. Whatever you do, you don't want the plastic to smoke. Once it starts to smoke, you've gone above the working temperature of the plastic, and the repair will be very brittle. Also, UV light has a lot to do with the lifespan of the material, and for a boat that has lived its whole life in the sun, you'll notice significant fading of color and weakening of the plastic.
It sounds like you want to completely overhaul the hardware on the boat. If you've got your heart set on doing that you're probably better off buying a plastic welding kit. That said, the way that I've seen plastic repair done (for small cracks) is with a heat gun, a piece of filler plastic (they sell it in thin rods), and a putty knife. You'll want to clean the area around the cracks, and then bevel both edges so that there's a bit of a gouge that you will then fill with the filler plastic. You want to get the filler plastic soft enough that it will stick into the gouge and melt in with the original material. Stir the filler plastic in with the original stuff with the plastic rod until you get nice swirling patterns. The first round of this won't fill the entire crack, you'll take multiple (2-3) runs at it until the surface of the repair is as high or higher than the original. At this point, wait for it to cool, and trim it down so that it's flush with the rest of the boat.
Generally speaking, on a plastic boat, the hardware is at least half of the original manufacturing cost. The plastic/molding process is relatively cheap compared to stainless steel, bungee cord, and fittings. I'm not absolutely sure that the Malibu fittings are stainless steel, but I would certainly hope so. If they are, could you just replace the external bits? That would save you a lot of time, effort, and money. Also, you probably already know this, but stainless steel is just that...stain less steel. It isn't rust-proof, just more rust resistant.
You say that you want to remove the nut-serts and start from scratch. The reason that most companies are doing nut-serts instead of regular external/sandwich nuts and bolts is because it's damn near impossible to get a wrench up and inside of the hulls of most SOT kayaks...
I hope that all this helps...I guess it's kinda a lot.
Cheers,
West