The sysex messages are single messages, not a long stream. It’s not a patch data dump (there is no patch memory), it’s messages to configure the pitch bend range (0-12) and the autoglide range (0-24). For some reason, these can not be set from the front panel of the synth while most of the settings like key tracking, LFO clock sync, envelope retrigger mode, etc. can be. Otherwise I wouldn't even be messing around with the sysex.
I captured the sysex using MIDI Monitor. Double clicking on the message opens up an inspector window that allows saving the contents in .syx format. I then loaded that file into Sysex Librarian which can convert and export it as a .mid file.
I sent the sysex files direct to the Behringer synth from Sysex Librarian. I then sent the MIDI files using Sweet MIDI Player Pro and that worked. The two files in the “recently played” pane are the same two I imported into Logic for setting the pitch bend range.
When the regions are played by Logic,MIDI Monitor shows nothing being sent. It does see the MIDI clock messages.
I have a workaround but it would be nice if Logic would send the sysex. That way the settings of the synth are saved in the project itself.