I never position the basket under the strainer. I turn my snares off quite often and it just gets in the way. Plus, it pulls on the strings and causes the snare to be off center of the drum.Change the position of the snare stand,so there's nothing under the share strand end tabs.The term"double braced",applies to the legs,not the basket.Snare baskets will ,most of the time ,flex under pressure,unless they are custom made to accept very heavy cast shelled drums,like the Tama bell brass.
I'm using the Gibraltar 9606 Ultra Adjust Snare Stand and the way it's built seems pretty bulletproof. You're probably right though, it could be flexing enough to put pressure on the snares. Next time I jam I'll set it up completely out of the way of the snares.
That said, I'm still puzzled man, the aquarian high energy head might be what I need to solve the problem.