I’m wondering about the decision to release the fonts in TTF format only, because the conversion quality of the TrueType curves is not very good. The source PostScript UFOs look good, but the TT curves could be better even with the same number of control points.
I suspect that the Hbar and Tbar in Didot, Baskerville, Bodoni and Big Caslon are later additions that have not been carefully designed to match the other similar letters. Eth is part of the old Windows and Mac encodings, while Hbar and Tbar belong to the "Latin Extended" character set.
I’d say it also depends on what your plans are for your redesigned typeface. If you have a design project you would like to use the original typeface for, but can’t because of its shortcomings, I’d say it’s fine to make your own version of it. But if you want to release it commercially, and thereby ‘attacking’ the original design’s market share directly, I’d be really cautious.
Contacting the original designer may be a good option. Perhaps they would be happy to have someone improve an old design of theirs (if they agree with your assessment of the typeface’s faults).