If you told people you were looking for a modern retelling of the original version of King Arthur, they’d likely assume you meant a pseudo-historical one and would most likely direct you towards Mary Stewart’s Arthurian series: The Crystal Caves, The Hollow Hills, The Last Enchantment, and The Wicked Day. The first three star Merlin while the final one focuses on Mordred, and they’re the most famous Arthur stories that are grounded in the actual 5th century rather than Mallory’s pseudo-middle ages with knights and tournaments and whatnot.
So, how “Welsh” are they? Most “historical” takes on Arthur (such as Jack Whyte’s Dream of Eagles series, Marion Zimmer Bradley’s Mists of Avalon, or that abysmal 2004 King Arthur movie) have utterly no interest in incorporating the original sources, instead either just placing the Mallory stories in a more historical context or going off in their own direction – basically just telling a piece of historical fiction and then slapping the “Arthur” tag on it. However, Mary Stewart’s jump-off point actually is a medieval text, though not really a Welsh one: Geoffrey of Monmouth’s History of the Kings of Britain.
The Crystal Caves is a pretty faithful adaptation of all the Merlin parts from the History, with various extra bits that explore Merlin’s childhood and education, presenting a compelling figure who is basically a proto-scientist. As with the History, basically Merlin’s only supernatural abilities and all his other “magic” is accompanied through knowledge of engineering and herbalism, and the occasional exploitation of superstition. Its various references to Welsh culture and folklore feel valid, and its reliance on pre-Romantic sources does mean that even if doesn’t always feel quite mythological, it doesn’t usually feel very Mallory.
The later books do move away from the History (mainly because they are about Merlin’s relationship with Arthur, even though Geoffrey never had them meet), and thus draw more on the later Arthurian Romances, though Stewart also incorporates elements from Welsh folklore, such as the idea of there being more than one Guinevere, that Mordred was not entirely villainous, and that King Arthur’s sword was previously Emperor Macsen’s (an interesting choice, especially because “The Dream of Macsen Wledig” is actually the one native tale from the Mabinogion that normally has nothing to do with King Arthur). However, some of the Welsh elements are merely window dressing, such as Stewart changing Lancelot’s name to “Bedwyr,” so that she can still have the Lancelot-Guenevere-Arthur triangle but feature a warrior with a more authentically Celtic name.
Though reading Mary Stewart’s books won’t give you a good feel for early Arthurian mythology, it does a good job exploring the culture of that time period and adding various tidbits of folklore when it suits her purpose. In fact, with the exception of direct adaptation of folklore, such as Dr. Gwyn Thomas’ marvelous Quest for Olwen, Mary Stewart’s works is probably the most authentic stuff out there, and certainly some of the most well-written.