The described recording project [160410 MMDigest] does indeed sound
like fun, and I hope you find the roll you seek!  To momentarily assume
the mantle of Devil's advocate (or perhaps wet blanket) -- if the goal
is simply to hear the difference between the modern (but incorrect)
Equal Temperament (ET) and a given Unequal Temperament (UT, e.g.
Lehman), then there are numerous examples for Bach's WTC and otherwise
readily available on the Web, already recorded for posterity.

Furthermore, there is no consensus on the veracity of Lehman's
hypothesis concerning Bach's WTC tuning, mostly because there is no
evidence thereof.  Ref.:

https://en.wikipedia.org/wiki/The_Well-Tempered_Clavier#Title_page_tuning_interpretations 
http://my.ptg.org/blogs/fred-sturm/2014/10/24/lehman-bach-tuning-refuted 

Finally, while the WTC may have been written with more than one keyboard
instrument specifically in mind, it was certainly not composed for an
Ampico reproducing piano, rendered in early 20th Century performance
practice.  The point I am trying to make is that authenticity is a
relative proposition.

Now that I have been rather a grinch, I do wish you and your ill friend
well in your adventures...sincerely!

Ian Gillis

 [ It seems to me Bach's music and tuning temperament is best judged
 [ when played on the instrument it was composed for, not the modern
 [ piano.  -- Robbie