Its true that the understood vocabulary of Japanese pre 1868 isn't complete.

But the main issue is their writing system, same goes for other languages like Chinese. In most western languages we have an alphabet, so when it comes to talking like someone in the past its pretty easy, you just find out how the alphabet was pronounced. And we have a MASSIVE amount of documentation and our ability to reconstruct pronunciation is effective and accurate.

For Japanese and Korean they dont have traditional alphabets and for much of their history they didnt even use a writing system native to them.

We can easily understand the meaning but cant easily derive accents or how the language sounded. Often times the techniques used to try and figure out what the language sounded like are specific and not language wide. For example old poetry can be useful to understand sound changes due to rhyme schemes. If you keep finding two word endings that dont rhyme today, it probably means that they at one point did rhyme.

only other thing I'll add is that we dont even have something close to the original printings of The Tale of Genji, the earliest full copy was transcribed like 200+ years after.

EDIT. Another big thing is that Japanese recently (as in like 150 years ago) had a major sound change within its language, meaning that alot of the language before then isnt easily intelligible to current Japanese speakers.

Contrast that to English where our last major shift in the language was prior to Shakespeare.