The output is what I want -- flat beams at the exact same vertical position for all three beam figures.
BUT, what's bothering me is that setting Beam #'positions = #'(7.5 . 7.5) before the third figure is entirely "by eye". The first note of the third figure changes to the LH staff and, for this reason, the Beam positions of the third figure are relative to the LH staff (rather than to the RH staff, as with the first two figures). What I really want is a way to set Beam positions for the third figure reltiave to the RH staff rather than the LH staff (meaning that I wouldn't have to set beam positions by eye at all).