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a face full of splinters.
That's a horrible story, I hope you're ok now.
It's reassuring to hear that changing setup won't help, because I just got those wheels and I really enjoy how they ride. Plus, I wanted something a bit more versatile for road crits (only training for now), outdoor track (HH) and indoor (LVV). So I am glad that you're giving me the confidence to stick to clinchers.
For sure, every time I ride from now on I will inspect that the tube sits properly inside the tyre. And for sure I will switch to butyl tubes. One reason that surprised me of those latex tubes is that they deflate very quickly (almost completely over night), so you find yourself inflating them often, which increases the risk of pinching the tube.
I can assure you, from experience, tubs can also blow up on the Velodrome. Also I've been the victim of someones tub rolling off without even puncturing and ended up with a face full of splinters.
There's not much to choose between tyre performance at amateur racer level. If you really want to spend money on changing wheels and tyres over from your current setup to another setup, that's up to you, but I don't think you'll find much difference in performance or safety. You're still dealing with pressurised air inside rubber. :)