The pembridge helm is very different helm than the one linked. Late 14th century Great Helms seems to have much more rounded features than their boxy predecessors. What may seem like small stylistic differences can mean the difference of 50 or 100 years or more. Even then, by this time as Aiden mentioned, the great helm was largely relegated to the tourney field. It would eventually morph in to the Frogmouth helms of the mid 15th century.
What I would suggest is if you like a particular helmet, or style of armor that you decide you want to base your kit around, then do just that. For example, if you love that style of helmet, than maybe a 13th century kit is what you're really after. Don't try to force armor in to an arbitrary time period if you're interested in historical accuracy. Just shift the time period to match the style of armor you're interested in.