Thanks for the reply, Dan. If anyone on the team is ever interested in hearing the difference for for quality control purposes, just load both apps on a device (again, an iPad 3 can open both), switch between the apps playing the same song, and the difference will be apparent.
I will say that the difference is most pronounced when using the profile over AirPlay where BDPS has a separate device type for AirPlay, where JA uses “Speakers” as a device as there is no separate AirPlay option. Maybe that is causing the difference.
In any case, thanks again for the response. I enjoyed the BDPS app while it lasted and am glad I still have a device where it works.