wheel/tire advice

[Tickdoc]

I have an old set of ENVE 3.4 (non-ses) that I bought new from a dealer in 2012.

They've been my fast go to wheels forever now, but they don't seem to like the tires I seem to like. (veloflex master and vittoria corsa G). They are well out of warranty so I'm not sure Enve would do anything towards a new set, unless they offer the trade-in program again.

The beads pop out. Never a good thing. I can usually get a new set of corsas to mount if I'm careful, but I'm sick of having bead-seat anxiety. Roadside CO2 repairs are nearly impossible to set.

What's a good alternative fast yet supple tire to try that might have a more robust enve friendly bead? I had a blow-out this week and I have a trip coming up that I was going to use them on.