The parabolic reflector design does look reasonably robust to me; the bottom third of the LED encapsulation is still well socketed into the reflector. If the light is potted, it won’t be possible to push the LED backward into the driver cavity or bend it sideways, either.
It might not be quite as indestructible as the deeper-set arrangement of the Fenix E01, but it should still be pretty solid.
However, a standard parabolic reflector with the LED chip at the focus may not behave as expected with a 5mm LED, because the LED encapsulation is not curved for the light to arrive at right angles to the boundary between the encapsulation material and the air, which is what you need to avoid unwanted refraction.
Instead of having a hemispherical dome centred on the LED chip like a power LED does, a 5mm LED has a cylinder with a hemispherical dome on top. This is liable to bend the light path as it moves from the LED encapsulation to the air, so different parts of the parabolic reflector will see the light appearing to arrive from different points with a range of apparent offsets from the reflector focus. This means it will never form a collimated beam, no matter what you do.
In short, I suspect that the parabolic reflector will produce a fairly horrible beam pattern. I’d still be interested in seeing a picture of the actual result, though, just to make sure
I also suspect that the deep-set position of the E01’s LED in its conical reflector sidesteps the effect of varying light paths by simply discarding all light exiting the sides of the LED encapsulation.
I presume that it would be possible to create a reflector curvature that would compensate for the refractive effect of a 5mm LED’s encapsulation, but making such a bespoke reflector would be astronomically expensive by flashlight standards. It would also be thrown off by variations in the 5mm LED shape from one LED manufacturer to the next.
Personally, I’d be inclined to stick with an E01-style conical reflector, on the basis that we already know it works.