Hi Dogperson,
What I really like the music rack on top of this other Chickering of Liszt's [I think these are two different Chickering grand pianos]:

That piano [or those pianos] are, as you say, at the Liszt Museum in Budapest. Quite impressive is the Bechstein concert grand at the Liszt-Haus in Weimar, and which was used for his master classes:
I don't think the master class Bechstein is parallel strung, so I assume Barenboim's piano - which I don't know much about - is based on one of the others, or possibly even the other Bechstein grand at the Liszt-Haus, and which is parallel strung:

Or it could be based on the light brown Liszt Bechstein which tours around a lot.
Maybe you or someone else here knows which of these pianos is the model for Barenboim's instrument?
Mvh,
Michael