F&W Regs
Addressing the original question, if you're a person who likes to practice C&R, hooking fish deeply would cause more damage than a quick release of a fish hooked in or near the mouth. With that in mind, the choice off fly/lure is easy (based on the choice of egg patterns or pegged beads by the original poster). I would choose the fly/lure that in my experience causes least damage to fish.
As to the regs, perhaps the reason for ambiguity in defining what is a fly is due to the vast number of differing opinions about what is a fly and the fact that fly patterns and materials have been and continue to edvolve. Considering the difficulty in defining what is a fly, I'm not surprised that DFW chose a simple description.
According to the section of the regs describing snagging, (paraphrasing) if a fish is hooked outside the mouth it has been snagged and must be released. The intent of the fish in striking the lure has absolutely nothing to do with it and, unless you're using a fly/lure that is actually defined as illegal in the code, the fly/lure doesn't figure into the definition of snagging either. IMO, this only becomes an issue for enforcement if you're hooking fish outside the mouth and keeping them.
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