Chinstraps on pre-Rennissance and Rennissance helmets seems to be a fairly obscure subject... do you think the modern reproduction buckled-chinstraps resemble what would have been used in period?

This is typical for sallets.

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Information is difficult to find because the best solution wasn't a chin strap. It was a proper fitted or adjusted liner. Tournament helmets were sometimes laced down to the torso at various points for extra steadiness.

A liner is vitally important, but even very fine sallets had chin straps, so they can't be considered a second-best or low-rent solution. Rather, they would have been part of a complete suspension system that includes a properly fit helmet (first and foremost,) the lining band and the properly adjusted padded linen liner. In my limited experience researching and making an historical-style suspension system, these elements work together in subtle ways that make them dependent on each other.

I agree very much with Sean's comment. I have found that no matter how well it is fit the helmet does not stay in its exact place without a strap. I have tried getting the liner so tight that it was basically painful and still the helmet would move enough that it was not effective. The only helmets I figure that may not have had them are true closed helmets and those that fix to breastplates.

RPM

Thanks for the photograph, interesting to see that the buckes haven't changed much.
Without a chinstrap, even a good fitted helmet is not as secure as it could be.
I've actually never worn a reproduction helmet with a liner or strap, though I notice more modern military-style helmets are prone to falling off if left un-straped, regerdless of how well it fits. (while moving about/jumping, of course.)