No need for you to decide, as the Alter Rebbe already settled this after sorting through 60 siddurim. Your wisdom lies in upholding the words of the sages. Your explanation aligns with the one offered by the Shaar Hakolel. No need to apologize for discussing the above, as resolving doubts is part of upholding the words of the sages.
https://www.torahrecordings.com/rebbe/igroskodesh/012/005/4110