I've done a fair bit of plastic welding. On the farm I have one of those harbor freight plastic welding kits. Like welding metal there is a technique and it's kind hard to describe the how to, but you must have good penetration. With thick plastic sometimes it's best to try to weld from both sides going about half the depth on both sides. You HAVE to have filler material that is the same type of plastic being welded. If you use a different type of plastic for filler than you are welding it simply won't stick together and will make a mess. If it is at all possible to sacrifice a bit of plastic off another area of what you are welding that is what I like to do.
As for the kits, the HF kit does ok, my biggest complaint is that it is slow. As in it'll take you some time to fix a piece of plastic like that and it's not all that hot so it's unlikely you'll smoke it. At the shop, we have a table top soldering station was like a $500 setup 10 years ago. I bought tips for the soldering station for doing plastic welding and that thing is awesome to use. It gets plenty hot and easily melts the plastic, you can change heat settings to what you want, but of course it'll get hot enough to fry your plastic. It does take some practice to get good at plastic welding but once you get it down it'll be stronger than any adhesive and you can get the finished product nice and smooth which is great if it's something that will be seen. Hit the rest of the plastic with a heat gun or some fine steel wool with a lubricant, (like soapy water or mild cleaner) and next thing you know it'll look almost new, but yes it takes practice to get to that point.
The biggest problems are, if you overheat the plastic it'll be brittle, (unlikely to do that with the HF kit). And if the plastic is brittle it may break again nearby, but you can get really artistic with it and reinforce if from the back side.
However for your repair I'd drill a small hole at the end of the crack, and use epoxy and probably drill a couple more holes to run zipties in to strengthen that area. It's a simple solution, that doesn't require you learn a new skill that in all likely hood you'll seldom use, and it's for a part that isn't really seen. If you have the extra cash at $15 it might just be best to replace them, but for me I can't afford nothin' extra without working extra, so I'd probably repair the existing ones.
