Try to get a sample pack of Stoma Seal and Aqua Seal from Costa Medical. It's not free, but VERY low cost. The Stoma Seal is a thin membrane (I believe it might have adhesive on both sides, I don't remember) that goes between your wafer and your skin, and provides a secure base for the faceplate to adhere to. Aqua Seal is also a thin memberane, waterproof, and goes on over your faceplate and beneath your pouch (you cut the opening to the size of the pouch opening), and extends about an inch or so beyond the edges of the faceplate. If you have any leaks or breakthroughs, they are contained by the Aqua Seal until you can change your appliance.
You kept saying you "blew out your bag". I'm not quite sure where your leak is occurring. My assumption was a breakthrough between your faceplate and your skin. The Stoma Seal and the Aqua Seal should help enormously with that if my assumption is correct.
Also, if you use an adhesive remover wipe in order to remove your faceplate, you need to make sure you follow up with a plain water wipe or wet washrag to remove the last vestiges of the residue left by the remover wipe. If you don't your faceplate will never stick properly. I use Uni-Solve adhesive removaal wipes followed by flushable moist wipes to remove the Uni-Solve. Fan with something to ensure your skin is COMPLETELY dry and not sticky or tacky in any way, before putting on your faceplate or the Stoma Seal.
You mention only Convatec brand appliances, but I have never had much luck with them. I use Hollister New Image 2-piece with filtered pouches which snap in place with an audible click, and have had a lot of luck with them.
At any rate, hang in there, keep trying new things until you find what works best for YOU, and best of luck. Remember that it takes several weeks to figure out what works and what doesn't, and for your skin to get used to everything that is happening to it. Before too much longer, you'll be wondering what all the angst was about, as you go about your day without any hindrance.