I have two Islands and the plastic of kayaks do appear to be easy to work with for structural repair or worn areas. I did my first repair to my yellow 2009 Island and it was more difficult area to reach and work but it turned out awesome and has held up very strong. The location was in ama insert area. The plastic for some odd reason had spiral fracture and also lip cracked spiral that aka rest on internally in ama. The plastic looked a little thin in area so may have been a manufacture issue which can happen at times with molding but easy to fix. I used small thin mesh wire for structure and cut into shape and worked into plastic to rebuild lip for aka to sit on in ama. I then added yellow scrap plastic on top of mesh and sanded a little and kept fitting aka into ama as I worked to make sure would still fit. I then added a small amount of G-Flex epoxy to coat everything but probably not needed. This repair job is a little bit more snug but still operates very well and has held up at least 15 days out sailing last year with no negative issues. This repair did take awhile since I wanted to keep fitting pieces together to make sure I did not have any clearance related issues. Be careful when melting mesh into plastic as not to push it in too far and deform the plastic and existing structure. Mesh just needs to melt in enough to be close to flush then add thin layer of plastic. Its like the mesh acts like rebar in cement as it does in plastic.
For other style of repairs I would check whitewater kayak forums since those boats go through extreme abuse. Some seem to favor Gorilla tape, G-flex epoxy, bitchathane and welding plastic. I am trying to get into whitewater and have a few Jackson whitewater kayaks and plastic to my understanding on my two whitewater boats I have use different type of plastic so more difficult to repair and maybe unsafe to try to weld with fumes. So it may be important to do some research on type of plastic you have before starting repair.
My other repair has been to 2011 tandem island. I thought about using mesh at first but then decided not to since it has not cracked all the way through yet. Repair area is close to worn down on top right side of drain plug if boat upside down looking from rear. Boat probably would not survive another hit or scrub in area and it would be in for more difficult structural repair around metal drain insert. If it cracked around insert I probably would have removed insert and built boat up internally with mesh and then moved to the outside to work on hull. For this repair I went ahead and kept adding scrap plastic to build up and shape back to the existing structural lines of main hull.
I just use an old cheap soldering iron for my tool but it takes awhile so don't plan on being in a rush job when working plastic into place. Plastic I have been using has been labeled HDPE that I cut into strips. Obviously if you want nice looking repair try to get same scrap plastic and color from another boat. My scrap yellow plastic repair job the yellow does not match Hobie yellow real well. The Tandem red Island does not match with clear and what little scrap of red I found so if I get some Hobie red or yellow I would add a thin layer to color match the repair job a little better. I am sure fumes would not be healthy so you may want to do this outside or open up the garage doors for ventilation. Its easy to repair and shape but does take some patience.