I have spent a good deal of time with the basket hilt broadsword. First, the term "claymore" actually sees more period use in association with the baskethilt rather than the two handed sword. In fact, one of the few references to the two handed sword being called a "glaymore" {sic} is by two English men on vacation through the Highlands in the late 18th century- long after this type of sword had fallen out of use. (Johnson & Boswell: Journey to the Western Highlands of Scotland)
The manuals that we have of the Highland broadsword, I feel, do not depict as complete a martial art as the renaissance cut & thrust. These manuals, however, were mainly written by English, or by Scots who were trained by English or influenced by more southern styles. Also, many of the techniques in these broadsword manuals were also intended to be used with the lighter spadroons. I agree that many of the images from the Penicuik sketches (of which I have a copy) certainly suggest that a pre-1745 Highland style of fighting may have preserved more of it's medieval roots than the later regimental system that followed.
Another interesting aspect to think about is that following the Scots defeat at the Battle of Culloden in 1746, the English passed a series of Disarming Acts which forbade Scots from carrying and practicing arms. So you have a rising generation receiving no training in the Highland style. Soon after the British began to recruit from Scotland and began forming Highland Regiments. At this point, this was the only way young men could get weapon training...legally. They would have likely been trained in the English style in the forms that we see emerging at the latter end of the 18th century.
There is another interesting aspect that I had not thought about prior to John Clements fantastic article on footwear. In the early to mid 18th century many of the Highland commoners were usually barefoot or wore thin-moccasin like shoes. Usually cowhide with the rough hair facing outward. The fashion of the wealthy and what was used for footwear in the British military was a heeled and buckled shoe. John's article clearly shows that this type of footwear is not optimal for the dynamic and aggressive type of movements that are needed in a more efficient form of swordplay. If you take a time to try on a pair of these period shoes (and I have) you can see how they almost force you into more conservative and certainly more 2 dimensional movements. This is further proof of the degradation of sword fighting that was happening at this time.
So, long story not so short...if you want to learn to use it you can try to extrapolate techniques from the scant information of the pre-1745 sources. Or try the manuals from the period that seem to be a mid watered down from earlier styles of fighting. Look up Sir William Hope, Donald McBane, Thomas Page, Henry Angelo, Captain Sinclair, Thomas Mathewson for starters.
Now for the two-handed sword. There is loads of debate on this weapon being called a "claymore". The really short version is...we don't know. Most people know the term comes from the Gaelic "claidheamh mòr" meaning "great sword". But again, this term is mainly seen in the 18th century in reference to the baskethilt sword. There is some argument for the term “claidheamh da laimh" to be used for the two-handed sword. With so little written information in native Gaelic it's almost impossible to know without any further discoveries. Just for the sake of conversation I usually just say "scottish two handed sword" or "two handed claymore", just to get through the conversation. On a side note, there are some really cool scottish two handers with clamshell guards that further confuse things.
If information is scant on the pre-18th century use of the baskethilt, it is virtually non-existant on the earlier two-handed sword. The last recorded use we know of for this weapon was at the Battle of Killiencrankie in 1689. It would seem logical that it's use would mirror or closely resemble the longswords from mainland Europe. In fact, many if not most of the blades used in Scotland actually were shipped from Europe- places like Soligen and Prussia and some from Spain later on. The bare blades were sent to Britain where the local smiths would fit them with their hilts and such. It would seem likely that methods of use could easily be communicated that way. But that is just speculation. Best we can do without further discoveries is to work out with real intent, using quality replicas with good martial sense.
Hope my ramblings help.

"Why is there a picture of a man with a sword in his head on your desk?" -friends inquiry