Was "archaic Japanese" used to narrate historical anime series?
Unlikely.
Probably not the answer you're looking for but I also haven't watched every single historic feudal Japan anime so I can not definitely say for certain it doesn't exist.
Authors and script writers write for a modern audience who understand best a modern, living language. So it's rather unlikely that the majority of a work be entirely or heavily in an archaic language. Even for English, how many modern TVs or cartoons can you find that make heavy use of Modern English or better, Old English? I certainly cannot think of any aside from works inspired directly from classic works (Shakespeare, as mentioned, is a prime example).
There's a limit to how much archaic dialogue you give your characters. At best, characters are given occasional language quarks to remind the viewer of the setting but any more and you would lose the audience (or at least transform a light easily readable manga into a in depth literature analysis).
While I agree it would totally cool if there existed historical correct voice acting in anime or even manga written in ancient scripts, the appeal of these works is quite limited (think of the translation work for even the native speakers !)
I would also like to point out even within modern Japanese, people of different ages and regions speak very differently (not representative of voice actors in anime). While Kyoto used to be the capital of Japan, not Edo, even the current Kansai dialect differs from a historic accent. According to a few native Kansai, anime has poorly or inaccurately represented even their accents.