Like much that has gone before, not a lot of clarity in the murk. I911 Encyclopedia Brittanica is cited as saying two hander is, basket not so much.
It does note the term was at that time much used for both, though incorrectly applied to basket hilt. Don't know, don't own that edition. Couple
of sources note that American English says the term is accurate: great sword is the big one, Scots English favors basket hilt. I don't have a dog
in this hunt, was merely citing dictionaries as they are typically the arbiters of language questions. It may just be two peoples divided by a
common language.

Some think basket hilt may have become called big as it was larger and thicker (therefore more manly) than the swords used by English troops.
As with much history, much myth and differing opinions. In language, usage determines reality over time, so hold your own course.

I will note in passing I did not say the term went back to 1200; rather, gallowglass troops go back to latter half of that century. When they began
using two handers I don't know, but I think before basket hilts. Earliest I recall of illustrations is fairly early 16th century. Do not recall if claymore
was used as descriptor. I have doubts. What I have read indicates basket hilts began appearing later that century, I'm pretty sure McRob will
have a better idea than I about the timeline of arrival and usage in Scotland.

I know I will understand your basic intent whichever usage you choose.